Question

The angle of elevation of the top of a tower, whose height is 100 m, at a point whose distance from the base of the tower is 100 m is

• A. 30°
• B. 60°
• C. 90°
• D. 45°

Answer 1

The Correct Option is D

To solve the problem, we need to find the angle of elevation of the top of a tower from a point 100 m away from the base, given that the height of the tower is also 100 m.

1. Understanding the Right Triangle Setup:
In this scenario:

• Height of the tower (opposite side) = 100 m
• Distance from the point to the base of the tower (adjacent side) = 100 m

Let the angle of elevation be \( \theta \). Then: \[ \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{100}{100} = 1 \]

2. Solving for the Angle:
We know: \[ \tan 45^\circ = 1 \] So, \( \theta = 45^\circ \)

Final Answer:
The angle of elevation is 45° (Option D).