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Trigonometric Ratios in Right Triangles — Free MYP4 Mathematics (Extended) 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°.
a
Write down the trigonometric ratio that links the adjacent side, the hypotenuse, and the angle in a right triangle. [1]
b
Calculate the horizontal length of the roof section. [2]
c
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
8 marks~12 minCriterion D
A surveyor stands at the top of a cliff and measures the angle of depression to a boat at sea as . The horizontal distance from the base of the cliff to the boat is m. The surveyor models the cliff height using , where is the cliff height and is the horizontal distance.
a
Calculate the height of the cliff. Show all working. [3]
b
The angle measurement has a possible error of . Calculate the cliff height for and , and state the resulting range of possible heights. [2]
c
Advise the surveyor whether the model and a single angle reading are sufficient for reliable cliff-height measurement. In your advice, discuss how the angle measurement error affects the reliability of the result, identify at least two real-world factors that could reduce the model's accuracy, and justify your recommendation. [3]
Solutions
3QuestionSolving Word Problems with Right-Angled TrianglesAssessment Practice
8 marks~12 minCriterion D
A surveyor stands 50 m horizontally from each of five structures and records the following data.
| Object | Tree | Building | Flagpole | Cliff | Tower |
|---|---|---|---|---|---|
| Height (m) | 15.0 | 28.0 | 35.0 | 42.0 | 50.0 |
| Angle of elevation () | 16.7° | 29.2° | 35.0° | 40.0° | 45.0° |
a
Calculate for each object, rounding to 3 decimal places. Present your results as labelled rows matching the format above. [2]
b
Analyse the relationship between height and , using at least two numerical examples from your table as evidence. [2]
c
Deduce a general formula for height in terms of horizontal distance and angle of elevation . Apply your formula to find the height of a lighthouse observed at an angle of elevation of 53.1° from a point 50 m away. [2]
d
A safety regulation requires a warning beacon on any structure taller than 65 m within 50 m of a public path. Evaluate 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 records the horizontal distance (adjacent) and vertical rise (opposite) for three sight lines from a fixed base point.
The angle of elevation is measured from the horizontal.
| 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 is measured from the horizontal.
a
Calculate , , and , the angles of elevation for sight lines 1, 2, and 3. [3]
b
Deduce the angle of elevation for a fourth sight line where opposite = 4 m and adjacent = 5 m. Justify whether the angles of elevation are increasing at a constant rate. [4]
c
The surveyor requires an angle of elevation of exactly 45° to calibrate the camera. Analyse whether this calibration angle can ever be achieved using this sequence of sight lines, and evaluate what alternative measurement setup would be required. [5]
Solutions
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