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Trigonometric Ratios in Right Triangles — Free MYP5 Mathematics (Standard) Practice Questions
1QuestionUsing SOH-CAH-TOA to Find Missing SidesConcept Practice
4 marks~6 minCriterion A
A ladder leans against a wall. The diagram shows a right triangle where the ladder is 8 m long and makes a 35° angle with the ground. Study the diagram.
a
State which trigonometric ratio (SOH-CAH-TOA) links the angle, the hypotenuse, and the opposite side. [1 mark]
b
Calculate the height the ladder reaches up the wall. [1 mark]
c
Evaluate whether a ladder of the same length at 50° would reach more than 1 m higher, justifying your answer with calculations. [2 marks]
Solutions
2QuestionDefining 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
3QuestionUsing Trig Ratios to Find Missing AnglesAssessment Practice
3 marks~5 minCriterion C
A ladder leans against a vertical wall. The base of the ladder is 1.8 m from the wall, and the ladder reaches 3.0 m up the wall.
The graph below shows for .
The graph below shows for .
a
Explain how to use the graph to find the angle that the ladder makes with the ground. [1]
b
Determine the value of . [1]
c
A safety guideline states that a ladder is stable when the angle with the ground is between 70° and 80°. Advise whether the ladder is positioned safely, justifying your answer with reference to . [1]
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.
The angle of elevation is measured from the horizontal at the 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 is measured from the horizontal at the base point.
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, and justify whether the angles are increasing at a constant rate. [4]
c
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
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