Trigonometric Ratios in Right Triangles

You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 31 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Trigonometric Ratios in Right Triangles — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionUsing SOH-CAH-TOA to Find Missing SidesConcept Practice

4 marks~6 minCriterion A

A solar panel installation company assesses whether a roof section is suitable for fitting panels. The slant length of the roof is 15 m and the angle between the slant and the horizontal is 40°.

Write down the trigonometric ratio that links the adjacent side, the hypotenuse, and the angle in a right triangle. [1]

Calculate the horizontal length of the roof section. [2]

The installer states: "A horizontal span greater than 11 m confirms the roof is wide enough for the panel." Advise the installer whether the roof section should be approved for panel installation, justifying your answer with reference to your result from part (b). [1]

Solutions

2QuestionDefining Sine Cosine and TangentAssessment Practice

4 marks~6 minCriterion C

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

State the value of

\sin 30^\circ

and the value of

\cos 60^\circ

. [1]

Explain why

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

for all

\theta

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

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

3QuestionSolving Word Problems with Right-Angled TrianglesAssessment Practice

8 marks~12 minCriterion D

A surveyor measures the angle of elevation to five structures from a point 50 m away horizontally.

Object	Tree	Building	Flagpole	Cliff	Tower
Height (m)	15.0	28.0	35.0	42.0	50.0
Angle of elevation ( $\theta$ )	16.7°	29.2°	35.0°	40.0°	45.0°

Calculate

\tan\theta

for each object. Present your results as labelled rows matching the format above, rounding to 3 decimal places. [2]

Analyse the relationship between an object's height and its corresponding value of

\tan\theta

, using evidence from your table. [2]

Deduce a general formula for the height

h

of an object in terms of

\tan\theta

and horizontal distance

d

, then apply it to find the height of a lighthouse observed at an angle of elevation of 53.1° from the same point. [2]

A safety regulation states that any structure taller than 65 m within 50 m of a public path requires a warning beacon. Advise the safety inspector whether the lighthouse requires a warning beacon, justifying your decision with reference to the precision of your calculation. [2]

Solutions

4QuestionUsing Trig Ratios to Find Missing AnglesAssessment Practice

12 marks~18 minCriterion B

A surveyor uses a drone to photograph a hillside. The drone's camera records the horizontal distance (adjacent side) and vertical rise (opposite side) for three sight lines from a fixed base point.

Sight line 1	opposite = 1 m	adjacent = 2 m
Sight line 2	opposite = 2 m	adjacent = 3 m
Sight line 3	opposite = 3 m	adjacent = 4 m

The angle of elevation

\theta

is measured from the horizontal at the base point.

Calculate

\theta_1

\theta_2

, and

\theta_3

, the angles of elevation for sight lines 1, 2, and 3. [3]

Deduce the angle of elevation

\theta_4

for a fourth sight line where opposite = 4 m and adjacent = 5 m, and justify whether the angles are increasing at a constant rate. [4]

The surveyor needs an angle of elevation of exactly 45° to calibrate the camera correctly. Advise the surveyor whether this calibration angle can ever be achieved using the pattern in this sequence, and recommend what alternative measurement setup would be required. [5]

Solutions

Questions 5-35

Unlock these questions with Premium

That's every free question here — 4 of 35.

+31 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade