A man's eye level is 1.7m above the horizontal ground and 13m from a vertical pole. If the pole is 8.3m high…

Analyze the question

The man's eyes are 1.7 m above the ground, and the pole is 8.3 m tall. The horizontal distance from his eyes to the pole is 13 m. We need the angle of elevation of the top of the pole from his eyes.

Concept

The angle of elevation is measured from the horizontal line at eye level. This means we use only the height of the pole above eye level, and we use the tangent ratio:

tan θ = opposite / adjacent

Solution

1. Height of the pole above eye level: 8.3 − 1.7 = 6.6 m

2. Apply tangent: tan θ = 6.6 / 13 = 0.5077

3. Find the angle: θ = tan⁻¹(0.5077) ≈ 26.9°

4. Correct to the nearest degree: θ ≈ 27°

Answer: C (27°)

Tip

Always subtract the observer's eye height from the object's height before using tan. A common mistake is to use 8.3/13, which gives about 32.6° (option A or B, the distractors). Also remember that tan 27° ≈ 0.5095, which is very close to 0.5077, so this is a quick check.