Trigonometry — Free IB MYP5 Mathematics (Extended) Questions

1QuestionReal-Life Applications in Engineering and DesignConcept Practice

2 marks~3 minCriterion A

A bridge support is modelled as a right triangle. The horizontal distance from an engineer's observation point to the base of the support is 20 m, and the vertical height of the support is 15 m.

A diagram is provided.

a

Calculate the angle of elevation

\theta

from the engineer to the top of the support. [1]

b

The safety code requires that the angle of elevation of any bridge support, measured from an engineer's inspection point, must lie between 30° and 45°. Advise the engineer whether this support complies with the safety code, justifying your answer with reference to your calculated angle. [1]

Solutions

2QuestionUsing Scale and Bearings TogetherConcept Practice

4 marks~6 minCriterion A

A search-and-rescue team uses a map with a scale of

1:50\,000

. On the map, the straight-line distance between base camp

A

and a reported incident site

B

measures

8.4

cm. The bearing from

A

to

B

is

065°

.

a

Explain how the scale

1:50\,000

is used to convert the map distance to an actual ground distance. [1]

b

Determine the actual ground distance between

A

and

B

in kilometres. [2]

c

The rescue team can travel at most

5

km before requiring a resupply. Advise the team leader whether the team can depart from base camp

A

and reach site

B

without a resupply, justifying your advice with a numerical comparison. [1]

Solutions

3QuestionSketching Graphs of y = sin x cos x tan xConcept Practice

2 marks~3 minCriterion A

A coastal monitoring buoy records wave height. Engineers model the displacement (in metres) of the buoy from its rest position using

y = \sin x

, where

x

represents time in degrees over one complete cycle from

0°

to

360°

.

a

State the amplitude and period of

y = \sin x

, and identify the coordinates of the maximum, minimum, and all intercepts over this cycle. [1]

b

Explain what the amplitude and the minimum value tell an engineer about the buoy's motion in this context. [1]

Solutions

4QuestionSin and Cos rules based problemsConcept Practice

2 marks~3 minCriterion A

A surveyor measures a triangular plot of land,

ABC

. Angle

A = 35°

, angle

B = 72°

, and side

a = 8.2

cm (opposite angle

A

).

Calculate the length of side

b

, opposite angle

B

, using the sine rule:

\frac{a}{\sin A} = \frac{b}{\sin B}

Give your answer in centimetres, correct to 3 significant figures. [2]

Solutions

5QuestionProblem Solving with Non-Right TrianglesConcept Practice

2 marks~3 minCriterion A

A landscape architect is designing a triangular garden plot. The plot is modelled as triangle

ABC

, where

AB = 8

m,

AC = 5

m, and the included angle at

A

is

30°

.

A local regulation states that any garden plot smaller than

12 \text{ m}^2

requires an additional permit.

a

Calculate the area of triangle

ABC

. [1]

b

Justify whether the architect must apply for an additional permit. [1]

Solutions

6QuestionWorking with Two Sides and Included Angle SASAssessment Practice

4 marks~6 minCriterion B

A landscape architect designs triangular garden plots, each with two sides of lengths

a

and

b

and a fixed included angle of

35°

. The table shows how the area changes as the product of the side lengths increases.

$ab$ (cm²)	20	40	60	80	100	120
Area (cm²)	5.7	11.5	17.2	23.0	28.7	34.5

a

State the formula for the area of a triangle given two sides and their included angle. Hence calculate the constant of proportionality

k

when the included angle is

35°

. [1]

b

Analyse the data to show that area is directly proportional to

ab

, and determine the constant of proportionality from the data. [2]

c

The architect needs a plot with an area of at least 40 cm². Justify whether a plot with side lengths

a = 12

cm and

b = 11

cm is sufficient to meet this requirement. [1]

Solutions

7QuestionReal-Life Applications in Engineering and DesignAssessment Practice

4 marks~6 minCriterion D

A cable-stayed bridge has a vertical tower. A support cable runs from the top of the tower to a point on the deck. The cable makes an angle of elevation of

35°

with the horizontal. The horizontal distance from the base of the tower to the point where the cable meets the deck is

42

m.

a

Show that the height of the tower is given by

h = 42\tan(35°)

. [1]

b

Calculate the height of the tower, giving your answer to the nearest metre. [1]

c

A safety regulation states that the cable length must not exceed

1.5

times the tower height. Advise the bridge engineer whether this bridge satisfies the regulation, justifying your answer with a numerical comparison. [2]

Solutions

8QuestionUsing Given Side and Opposite Angle SSAAssessment Practice

3 marks~5 minCriterion C

A surveyor models a triangular plot of land as triangle

ABC

, where

a = 7

cm,

c = 5

cm, and

A = 70°

.

The graph below shows

y = \sin(x)

for

0° \leq x \leq 180°

, with a horizontal line drawn at

y = \dfrac{5\sin(70°)}{7} \approx 0.671

.

a

Identify the two possible values of angle

C

, rounding each to the nearest degree. [1]

b

Explain how the graph demonstrates that two distinct triangles are possible with the given information. [1]

c

The surveyor must choose the triangle in which angle

B

is obtuse. Justify whether this condition can be satisfied with the given measurements. [1]

Solutions

9QuestionUnderstanding Bearings as Directional AnglesAssessment Practice

6 marks~9 minCriterion C

A port is located at the origin

(0, 0)

and a lighthouse is at coordinates

(3, 4)

km, where the positive

x

-axis points east and the positive

y

-axis points north. A student proposes the following model to calculate the bearing of the lighthouse from the port:

\theta = \tan^{-1}\!\left(\frac{x}{y}\right), \qquad B = 90° - \theta

a

Calculate the bearing

B

predicted by the student's model. [2]

b

Construct the correct bearing using a clearly labelled diagram and trigonometric reasoning. [2]

c

The lighthouse is the destination of a vessel that must follow a bearing accurate to within

\pm 2°

to avoid shallow waters. Advise the navigator whether the student's model should be used for this voyage, identifying the source of any error in the model. [2]

Solutions

10QuestionDrawing Diagrams from Bearings DescriptionsAssessment Practice

8 marks~12 minCriterion B

A surveyor maps four survey stations P, Q, R, and S using the following bearings:

P to Q:

030°

Q to R:

120°

R to S:

210°

S to P:

300°

All bearings are measured clockwise from north.

a

Construct a clearly labelled diagram showing points P, Q, R, S and the four bearing lines. Mark a north arrow at each station and label each bearing. [2]

b

Deduce the interior angle at each vertex of quadrilateral PQRS using the bearing data. Present your results as four labelled values. [2]

c

Analyse the relationship between consecutive bearings and the interior angle formed at their shared vertex. Hence advise the surveyor whether this quadrilateral is suitable to represent a rectangular building plot, justifying your answer with reference to both the angle properties and the closure of the survey loop. [4]

Solutions

11QuestionDrawing Diagrams from Bearings DescriptionsAssessment Practice

6 marks~9 minCriterion D

A ship departs from port A and sails on a bearing of

060°

for 12 km to reach point B. It then changes course to a bearing of

150°

and travels 8 km to arrive at point C. A coastguard vessel at port A can only respond to emergencies within a 7 km radius.

a

Construct a diagram of the ship's journey. Include north lines at A, B, and C, and label all points and distances. [2]

b

Deduce the angle

\angle ABC

. [2]

c

The ship reports an emergency at point C. Advise the coastguard commander at A whether the vessel should be dispatched, justifying your answer with a calculated distance. [2]

Solutions

12QuestionDefining Sine Cosine and TangentAssessment Practice

4 marks~6 minCriterion D

A surveyor estimates the height of a vertical cliff. She stands 50 m from the base along flat horizontal ground and measures the angle of elevation to the cliff top as

30°

.

a

Calculate the height of the cliff using the tangent ratio. [1]

b

Explain why the tangent ratio is more practical than the sine ratio for this measurement. [1]

c

The angle measurement has an uncertainty of

\pm 2°

. Calculate the range of possible heights, then advise the surveyor whether her single estimate of 28.9 m is sufficiently reliable to report without qualification. [2]

Solutions

13QuestionDefining Sine Cosine and TangentAssessment Practice

4 marks~6 minCriterion B

A surveyor uses complementary angles when measuring elevation from two positions. The graph of

y = \sin \theta

is shown for

0^\circ \leq \theta \leq 90^\circ

.

a

State the value of

\sin 30^\circ

and the value of

\cos 60^\circ

. [1]

b

Explain why

\cos(90^\circ - \theta) = \sin \theta

for all

\theta

in a right triangle, referring to the sides of the triangle. [2]

c

Advise the surveyor whether the sine of an elevation angle and the cosine of its complementary angle can always be used interchangeably in the field, justifying your answer. [1]

Solutions

14QuestionDefining Sine Cosine and TangentAssessment Practice

2 marks~3 minCriterion D

A surveyor stands 40 m from the base of a telecommunications tower on level ground. Using a clinometer, she measures the angle of elevation to the top of the tower as 62°.

a

Explain how the tangent ratio is used to calculate the height of the tower, and state the height correct to one decimal place. [1]

b

Discuss one limitation of this method that affects the accuracy of the calculated height, and advise the surveyor whether she can confidently report that the tower meets a minimum height requirement of 75 m. [1]

Solutions

15QuestionUsing SOH-CAH-TOA to Find Missing SidesAssessment Practice

6 marks~9 minCriterion A

A surveyor needs to find the height

h

of a vertical cliff on the opposite bank of a river. From point A, the angle of elevation to the cliff top is

35°

. She walks

50\ \text{m}

directly away from the cliff to point B, where the angle of elevation is

25°

. Both points are at the same horizontal level as the base of the cliff.

a

Let

x

be the horizontal distance from A to the base of the cliff. Construct two equations using tangent ratios and solve the system to find

h

, rounded to the nearest metre. [3]

b

The surveyor's instrument has a precision of

\pm 1°

. Deduce the value of

h

when a

+1°

error is applied to the angle at A (using

36°

instead of

35°

), rounded to the nearest metre. [1]

c

The surveyor must report this height to a construction team planning to build a bridge. Advise the surveyor whether the trigonometric model alone is sufficient for this purpose, considering the assumptions made and the sensitivity of

h

to measurement error shown in part (b). [2]

Solutions

16QuestionApplications in Architecture and PhysicsAssessment Practice

9 marks~14 minCriterion B

The table shows the dimensions and space diagonal lengths for a sequence of rectangular prisms.

Prism number	1	2	3	4
Dimensions (cm)	$1\times1\times1$	$1\times2\times3$	$1\times3\times5$	$1\times4\times7$
Space diagonal (cm)	$\sqrt{3}$	$\sqrt{14}$	$\sqrt{35}$	$d_4$

The space diagonal of a rectangular prism with dimensions

l

,

w

,

h

is given by

d = \sqrt{l^2 + w^2 + h^2}.

a

Calculate the exact value of

d_4

, the space diagonal of Prism 4. Give your answer in the form

\sqrt{k}

, where

k

is an integer. [2]

b

Deduce a rule for

d_n

, the space diagonal of Prism

n

, in the form

d_n = \sqrt{an^2 + bn + c}

where

a

,

b

, and

c

are integers. State the values of

a

,

b

, and

c

. [3]

c

Verify your rule for Prism 3. Hence justify why the expression under the square root must be a quadratic function of

n

for every prism in this sequence, referring to the structure of the dimensions. [4]

Solutions

17QuestionApplications in Architecture and PhysicsAssessment Practice

6 marks~9 minCriterion A

The diagram shows a right-angled triangle

ABC

representing a roof truss, where

\angle B = 90°

. The horizontal span

AB = 8

m, the vertical rise

BC = 3

m, and the hypotenuse

AC = h

m.

a

Show that

h = \sqrt{73}

. [1]

b

A second roof truss is geometrically similar to the first. Its hypotenuse is

2\sqrt{73}

m. Find the horizontal span of the second truss, in metres. [2]

c

A third roof truss has the same horizontal span of

8

m but a vertical rise

r

m, where

r > 3

, and a hypotenuse of

\sqrt{89}

m. Find the value of

r

and hence justify whether this third truss meets a building regulation requiring a vertical rise of at least

5

m. [3]

Solutions

18QuestionApplications in Architecture and PhysicsAssessment Practice

9 marks~14 minCriterion D

An architect is designing a roof truss for a community centre. The truss forms an isosceles triangle in a vertical plane with a horizontal base of 12 m. The pitch angle (the angle between the base and each sloping rafter) is

35^\circ

. The ridge height above the base is

h

m and each rafter has length

r

m.

a

Show that

h = 6\tan 35^\circ

, and hence calculate

h

to 3 significant figures. Give your answer in metres. [2]

b

Find the rafter length

r

to 3 significant figures. Give your answer in metres. [2]

The architect uses the linear model

H(x) = x\tan 35^\circ

to predict the height (in metres) at horizontal distance

x

metres from the left support. After construction, three on-site measurements are taken.

x

(m): 3, 6, 9

Predicted

H(x)

(m): 2.10, 4.20, 6.30

Measured height (m): 2.61, 4.88, 7.43

c

Calculate the percentage error at

x = 6

m, using

\text{percentage error} = \frac{|\,\text{predicted} - \text{measured}\,|}{\text{measured}} \times 100\%.

Give your answer to 1 decimal place. [2]

d

Assess whether the linear model

H(x) = x\tan 35^\circ

is suitable for use in the final construction drawings, referring to the percentage errors at all three values of

x

and giving one reason why the measured heights may differ from the model predictions. [3]

Solutions

19QuestionApplications in Architecture and PhysicsAssessment Practice

6 marks~9 minCriterion C

A vertical pole of height 10 m stands on horizontal ground. A sun ray makes an elevation angle

\theta

with the horizontal, casting a shadow of length

L

metres along the ground.

The ratio

R

is defined as

R = \frac{10}{L}.

a

Write down the value of

R

when

\theta = 45°

. [1]

b

Calculate

R

to 3 significant figures for each elevation angle in the table below.

Elevation angle (degrees): 30, 40, 50, 60

Shadow length

L

(m): 17.32, 11.92, 8.39, 5.77

R = \dfrac{10}{L}

: ?, ?, ?, ? [2]

c

A student claims that

R = \tan(\theta)

for any elevation angle

\theta

. Justify this claim using your completed table, and hence deduce whether the model

R = \tan(\theta)

is reliable enough to predict shadow behaviour at

\theta = 70°

for a solar panel alignment system that requires predictions accurate to 3 significant figures. [3]

Solutions

20QuestionApplying the Cosine Rule to Find Sides or AnglesAssessment Practice

8 marks~12 minCriterion B

The diagram shows three figures in a growing pattern made from right-angled triangles. Each triangle has shorter sides

a

and

b

and hypotenuse

c

, where

a

,

b

, and

c

are positive integers.

Figure 1	$a = 3$	$b = 4$	$c = 5$
Figure 2	$a = 5$	$b = 12$	$c = 13$
Figure 3	$a = 8$	$b = 15$	$c = 17$

a

Show that

a^2 + b^2 = c^2

for Figure 1, and write down the value of

c^2 - b^2

for Figure 2. [2]

b

Deduce the values of

b

and

c

for Figure 4, given that

a = 11

, by first describing the pattern in

c - b

across Figures 1, 2, and 3. [3]

c

A student claims that every figure in this pattern satisfies

c = b + 1

. Justify whether this claim should be accepted, and find the value of

a

for a figure in this pattern where

b = 20

. [3]

Solutions

21QuestionApplying the Cosine Rule to Find Sides or AnglesAssessment Practice

8 marks~12 minCriterion C

Triangle

ABC

has fixed sides

a = BC = 5

cm and

b = AC = 8

cm with variable included angle

C

.

The cosine rule gives:

c^2 = 89 - 80\cos C

where

c = AB

is measured in cm.

a

Complete the table below, giving each value of

c

correct to 2 decimal places where necessary.

C

:

30°

\quad

60°

\quad

90°

\quad

120°

c

(cm): \_\_\_\_

\quad

\_\_\_\_

\quad

\_\_\_\_

\quad

\_\_\_\_ [2]

b

As

C

increases from

30°

to

120°

, explain how

c

changes and why this behaviour is consistent with the expression

c^2 = 89 - 80\cos C

. Your explanation must refer to the behaviour of

\cos C

over this interval. [3]

c

A student claims that

c

when

C = 150°

is greater than

c

when

C = 120°

. Calculate

c

when

C = 150°

, giving your answer correct to 2 decimal places. Hence justify whether the student's claim is correct by referring to how

\cos C

changes as

C

increases from

120°

to

150°

. [3]

Solutions

22QuestionApplying the Cosine Rule to Find Sides or AnglesAssessment Practice

5 marks~8 minCriterion A

The diagram shows triangle

ABC

with

AB = 8

cm,

BC = 11

cm, and

AC = 14

cm.

a

State which angle of the triangle is the largest, giving a reason. [1]

b

Calculate the size of angle

ABC

. Give your answer correct to 1 decimal place. [2]

c

A student claims that a triangle with sides

8

cm,

11

cm, and

k

cm has its largest angle equal to exactly

90°

. Find the value of

k

in exact form, and justify whether

k

is indeed the longest side of this triangle. [2]

Solutions

23QuestionFinding the Area of Any Triangle Using TrigonometryAssessment Practice

6 marks~9 minCriterion D

A surveyor models a triangular plot of land with two measured sides

a = 150

m and

b = 200

m and an included angle

C = 40°

. The area of the triangular plot is given by

\text{Area} = \frac{1}{2}ab\sin C.

The diagram shows the triangular plot with the two sides and included angle labelled.

a

Calculate the area of the plot for

C = 40°

. Give your answer in m² to 3 significant figures. [1]

b

The surveyor's angle measurement has an uncertainty of

\pm 2°

, so the true angle

C

lies in the range

38°

to

42°

. Calculate the area of the plot for

C = 38°

and for

C = 42°

, and hence state the range of possible areas. Give your answers in m² to 3 significant figures. [3]

c

The land is gently sloping rather than flat. Justify whether the area calculated in part (a) is an overestimate or an underestimate of the true surface area of the plot. [2]

Solutions

24QuestionGraphing Real-Life Periodic PhenomenaAssessment Practice

6 marks~9 minCriterion B

The water depth (in metres) at a harbour is modelled over a 24-hour period. Measurements are taken every 2 hours.

Time (h)	0	2	4	6	8	10	12	14	16	18	20	22
Depth (m)	3.2	5.6	7.0	5.6	3.2	1.8	3.2	5.6	7.0	5.6	3.2	1.8

The depth is modelled by

h(t) = A\sin(Bt) + D

, where

t

is time in hours,

A

is the amplitude,

B

is related to the period by

\text{period} = \dfrac{2\pi}{B}

, and

D

is the vertical shift.

a

Justify that the period of the tidal cycle is 12 hours. [2]

b

Deduce the values of

A

,

B

, and

D

, and write the complete model for

h(t)

. [2]

c

A vessel requires a minimum depth of 5.0 m to enter the harbour safely. Using your model, advise the harbour master whether the vessel can enter safely at

t = 3

hours, justifying your answer with a calculation. [2]

Solutions

25QuestionSketching Graphs of y = sin x cos x tan xAssessment Practice

3 marks~5 minCriterion C

A sound engineer models the pressure wave of a pure musical tone using

y = \sin x

, where

x

represents time in degrees over one complete cycle (

0° \leq x \leq 360°

).

The function passes through

(0°, 0)

,

(90°, 1)

,

(180°, 0)

,

(270°, -1)

, and

(360°, 0)

.

a

Calculate

\sin 45°

, giving your answer in exact form. [1]

b

Deduce the values of

\sin 135°

and

\sin 225°

, using symmetry properties of the sine function. [1]

c

The engineer states: "The pressure wave is perfectly balanced — positive and negative peaks are equal in magnitude throughout the cycle." Using your results from (a) and (b), and the value

\sin 315°

, justify whether this statement is correct. [1]

Solutions

26QuestionGraphing Real-Life Periodic PhenomenaAssessment Practice

8 marks~12 minCriterion D

The water height at a harbour is modelled by

h(t) = 3.5\sin(0.52t - 1.57) + 4.2

where

h

is in metres and

t

is hours after midnight.

Actual measurements:

t

(hours after midnight): 2, 8, 14

Actual

h

(m): 2.1, 6.3, 2.3

a

Calculate the predicted water height at

t = 2

,

t = 8

, and

t = 14

. Show all substitutions clearly. [3]

b

Calculate the percentage error at each time using

\text{percentage error} = \frac{|\text{predicted} - \text{actual}|}{\text{actual}} \times 100\%

Show your working for each value. [3]

c

A fishing vessel requires a minimum water height of 3.8 m to enter the harbour safely. Advise the harbour master whether the model alone is sufficient to determine safe entry times, justifying your answer using the percentage errors from part (b). [2]

Solutions

27QuestionSin and Cos rules based problemsAssessment Practice

8 marks~12 minCriterion B

A surveying team records two side lengths and a non-included angle for four separate plots of land. For each plot, the team must determine how many distinct triangular boundaries are geometrically possible before construction can begin.

Plot A	$a = 8$ cm	$b = 12$ cm	$A = 30°$
Plot B	$a = 10$ cm	$b = 8$ cm	$A = 40°$
Plot C	$a = 6$ cm	$b = 10$ cm	$A = 25°$
Plot D	$a = 7$ cm	$b = 7$ cm	$A = 50°$

Here

a

is the side opposite angle

A

, and

b

is the other given side.

a

Calculate all possible values of angle

B

for each plot using the sine rule. State the number of distinct triangles possible in each case. [4]

b

Deduce a general rule, in terms of

a

,

b

, and

A

, that predicts when exactly two distinct triangles are possible. [2]

c

A construction permit is issued only when a unique triangular boundary exists. Justify which plots receive a permit, using your rule from part (b) and the geometry of the sine ratio to explain why ambiguous cases must be rejected. [2]

Solutions

28QuestionSin and Cos rules based problemsAssessment Practice

8 marks~12 minCriterion D

Two search-and-rescue stations, A and B, are positioned 50 km apart along a straight coastline. Station A records the bearing of a distress signal as

30°

from the coastline; station B records it as

50°

from the coastline. Each bearing has an uncertainty of

\pm 1°

due to equipment limitations.

a

Show that the distance from station A to the signal is approximately 38.9 km, using the Law of Sines with exact bearings of

30°

and

50°

. [2]

b

Deduce the maximum possible range of distances from station A to the signal when the worst-case bearing errors of

\pm 1°

are applied simultaneously at both stations. [2]

c

A rescue coordinator must decide whether two-station triangulation is reliable enough to direct a rescue vessel in rough seas. Advise the coordinator whether this method should be used alone or combined with supplementary positioning, using your results from parts (a) and (b) and at least two real-world limitations of the model. [4]

Solutions

29QuestionSin and Cos rules based problemsAssessment Practice

2 marks~3 minCriterion D

A surveying team needs to find the straight-line distance across a river to a landmark

C

on the opposite bank. Direct measurement is impossible.

The team stands at two points,

A

and

B

, on the same bank, measuring a baseline

AB = 84\ \text{m}

. They record the angle to the landmark from each point:

\angle CAB = 71°

and

\angle CBA = 63°

.

Apply the Sine Rule to find the distance

AC

, then advise the team on whether a rope of length

110\ \text{m}

is sufficient to reach the landmark from point

A

. [2]

Solutions

30QuestionFinding the Area of Any Triangle Using TrigonometryAssessment Practice

4 marks~6 minCriterion C

A landscape architect is designing a triangular garden bed with two fixed side lengths

a = 9.2

cm and

b = 12.5

cm (on a scale drawing). The graph below shows how the area of the triangle varies with the included angle

C

, using

\text{Area} = \frac{1}{2}ab\sin C

.

a

Show that the area formula simplifies to

\text{Area} = 57.5\sin C

. [1]

b

Explain how the shape of the graph shows that the maximum area occurs at

C = 90°

. [2]

c

The architect claims a right-angled triangular bed gives the most efficient use of the fixed side lengths. Calculate the maximum area correct to 3 significant figures, and advise the architect whether this right-angle design should be adopted to maximise the garden bed area. [1]

Solutions

31QuestionProblem Solving with Non-Right TrianglesAssessment Practice

6 marks~9 minCriterion B

A triangular solar panel frame is being designed with two fixed struts of length 10 cm and 14 cm. The included angle

C

between the struts can be adjusted during assembly.

a

Using

\text{Area} = \frac{1}{2}ab\sin C

, calculate the area of the triangle for each angle below. [2]

Angle

C

(degrees): 20, 40, 60, 80, 100

Area (cm²): ___, ___, ___, ___, ___

b

Describe the pattern in the areas as

C

increases from 20° to 100°, and deduce the angle that produces the maximum area. [2]

c

Justify the engineer's claim that

C = 90°

produces the greatest area, using the behaviour of

\sin C

, and advise the assembly team on how to set the struts and what happens to the enclosed area if they deviate from this angle. [2]

Solutions

32QuestionFinding the Area of Any Triangle Using TrigonometryAssessment Practice

8 marks~12 minCriterion D

A homeowner measures two sides of a triangular roof section for solar panel installation:

a = 6.8 \text{ m}

and

b = 5.2 \text{ m}

, with included angle

C = 72°

. The tape measure has accuracy

\pm 0.05 \text{ m}

and the protractor has accuracy

\pm 1°

.

\text{Area} = \tfrac{1}{2}ab\sin C

a

Calculate the area of the triangular roof section. [2]

b

Analyse how the measurement uncertainties affect the estimated area by calculating the maximum and minimum possible areas. [3]

c

Advise the homeowner whether the calculated area alone is sufficient to determine how many solar panels to order, identifying at least two limitations of the triangular model. [3]

Solutions

Trigonometry — Free MYP5 Mathematics (Extended) Practice Questions