Question

The angles of elevation of an electric pole from two points A and B lying on the level ground on either side of the pole are 30° and 60° respectively. If the two points A and B are 500 m apart, then at what distance from point A is the electric pole?

• A. 120 m
• B. 125 m
• C. 375 m
• D. 380 m

Hint:

When angles of elevation are given from two opposite sides, always equate heights using tangent ratios.

Answer 1

The Correct Option is C

Step 1: Let the pole's height be \(h\).
Let distance from A to pole = \(x\). Then distance from B to pole = \(500 - x\).
Step 2: Use tan ratios.
From A: \( \tan 30^\circ = \frac{h}{x} = \frac{1}{\sqrt{3}} \Rightarrow h = \frac{x}{\sqrt{3}}.\)
From B: \( \tan 60^\circ = \frac{h}{500 - x} = \sqrt{3} \Rightarrow h = \sqrt{3}(500 - x). \)
Step 3: Equate heights.
\(\frac{x}{\sqrt{3}} = \sqrt{3}(500 - x)\).
Multiply by \(\sqrt{3}\): \(x = 3(500 - x)\).
Solve: \(x = 1500 - 3x \Rightarrow 4x = 1500 \Rightarrow x = 375.\)
Step 4: Conclusion.
The pole is 375 m from point A.