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Trigonometry: angles of elevation and depression — KCSE Mathematics

KCSE Mathematics · 108 practice questions · 3 syllabus objectives

38 easy37 medium33 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Define and distinguish between the angle of elevation and angle of depression and represent them in a diagram

Apply trigonometric ratios to solve problems involving angles of elevation, depression and bearings

Trigonometry: angles of elevation and depression

Sample Questions

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1
easySHORT ANSWER2 marks

From a point on the ground, the angle of elevation to the top of a tree is 30°. If the distance from the point to the base of the tree is 10 m, calculate the height of the tree. (2 marks)

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Part (a) — 2 marks
Use the formula h = d × tan(30°) (1 mk)
Height of the tree = 10 × (1/√3) = (10√3)/3 m (1 mk)
2
easySHORT ANSWER4 marks

Explain the difference between the angle of elevation and the angle of depression and describe their significance in real-life situations. (4 marks)

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Part (a) — 2 marks
The angle of elevation is measured upwards from the horizontal (1 mk)
The angle of depression is measured downwards from the horizontal (1 mk)
Part (b) — 2 marks
Angle of elevation is used by surveyors to measure the height of mountains or buildings (1 mk)
Angle of depression is used by pilots to determine the height of an aircraft above the ground (1 mk)
3
easySHORT ANSWER4 marks

Define the angle of elevation and the angle of depression. Provide one practical example for each. (4 marks)

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Part (a) — 2 marks
The angle of elevation is formed between the horizontal line and the line of sight when looking upwards at an object above the horizontal (1 mk)
Example: Looking up at a tall building from the ground (1 mk)
Part (b) — 2 marks
The angle of depression is formed between the horizontal line and the line of sight when looking downwards at an object below the horizontal (1 mk)
Example: Looking down from a balcony at people on the street below (1 mk)
4

From a point on the ground, the angle of depression to a car parked on the road is 45°. If the observer's height is 10 m, determine the horizontal distance from the base of the observer to the car. (2 marks)

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