A boy 1.4 m tall, stood 10m away from a tree of height 12 m. Calculate, correct to the nearest degree, the…

Analyze the question

A boy 1.4 m tall stands 10 m from a tree 12 m high. We want the angle of elevation of the treetop from his eyes. We treat the boy's height as the height of his eyes above the ground.

Concept

The angle of elevation is measured from the horizontal line of sight. Draw a right-angled triangle where:

• The horizontal side (adjacent) is the distance from the boy to the tree = 10 m
• The vertical side (opposite) is the height of the tree above the boy's eye level
• tan θ = opposite / adjacent

Solution

Step 1: Find the opposite side. Opposite = 12 − 1.4 = 10.6 m

Step 2: Apply tangent. tan θ = 10.6 / 10 = 1.06

Step 3: Find θ. θ = tan⁻¹(1.06) ≈ 46.7°, which is 47° to the nearest degree.

Check the other options: 70° would need tan θ ≈ 2.75, and 19° or 8° would give much smaller ratios (tan 19° ≈ 0.34, tan 8° ≈ 0.14). Only 47° matches.

Answer: B. 47°

Exam tip: In elevation problems, always subtract the observer's eye height from the object's height. Forgetting this step is a common trap. If you used 12 directly, you'd get tan⁻¹(1.2) ≈ 50°, which is not an option, so the options tell you the subtraction is needed. Also, tan 45° = 1, so a ratio just over 1 means an angle just over 45°.