Question

Two persons, on either side of a tower 45 m high, observe the angles of elevation of the top of the tower to be 30° and 60°, respectively. The distance (in m) between the two persons is:

• A. \( 45\sqrt{3} \)
• B. \( 60\sqrt{3} \)
• C. \( 60(\sqrt{3} + 1) \)
• D. \( 45(\sqrt{3} + 1) \)

Hint:

In such problems, break down the situation into triangles and apply trigonometric ratios like tangent and sine to solve for unknown distances.

Answer 1

The Correct Option is B

Let the distance between the persons be \( D \).
From the geometry of the situation, we know the angles of elevation and the height of the tower.
Using the tangent of the angles, we can write two equations: \[ \tan 30^\circ = \frac{45}{D_1}, \quad \tan 60^\circ = \frac{45}{D_2} \] Now, calculate the distances \( D_1 \) and \( D_2 \), and then find the total distance \( D = D_1 + D_2 \).