Question

If the angle of elevation of the top of a tower of height 100 meters from a point to its foot is \( \tan^{-1} \left( \frac{4}{5} \right) \), then what is the distance from the point to its foot in meters?

• A. 110
• B. 120
• C. 125
• D. 150

Hint:

In trigonometric problems involving heights and distances, use the definition of tangent: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \), and solve for the unknown distance.

Answer 1

The Correct Option is C

Let the distance from the point to the foot of the tower be \( x \). Given that the angle of elevation is \( \tan^{-1}\left(\frac{4}{5}\right) \), we have: \[ \tan \theta = \frac{4}{5} \quad \Rightarrow \quad \frac{100}{x} = \frac{4}{5}. \] Solving for \( x \): \[ x = \frac{100 \times 5}{4} = 125. \]