Question

An observer 1.5 m tall is 48.5 m away from a pole. The angle of elevation of the top of the pole from his eye is 45°. Find the height of the pole.

Answer 1

Given:

Observer’s eye height = 1.5 m

Horizontal distance from observer to pole = 48.5 m

Angle of elevation to top of pole = 45°

Let the pole’s total height = h m

Step-wise calculation:

1. The vertical height of the pole above the observer’s eye = h – 1.5.

2. In the right triangle formed. 

`tan 45^circ = (h - 1.5)/48.5`

3. Since tan 45° = 1, we get `1 = (h - 1.5)/48.5`.

4. Therefore, h – 1.5 = 48.5

⇒ h = 48.5 + 1.5

⇒ h = 50.0

Height of the pole = 50.0 m.