Solving Triangles with Given Information

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Solving Triangles with Given Information — Free MYP5 Mathematics (Extended) Practice 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.

Calculate the angle of elevation

\theta

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

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 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

Identify the two possible values of angle

C

, rounding each to the nearest degree. [1]

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

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

3QuestionWorking 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

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]

Analyse the data to show that area is directly proportional to

ab

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

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

4QuestionReal-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

Show that the height of the tower is given by

h = 42\tan(35°)

. [1]

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

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

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