Two men on either side of a temple of 40 m height observe its top at the angles of elevation 30° and 30°, respectively. What is the distance between the two men in meters?

Correct option is C

Given:

Height of the temple = 40 m

Angles of elevation from both sides =$$30^\circ$$​​

Both men observe the top from opposite sides at the same angle

Concept Used:
$$\tan \theta = \frac{\text{Perpendicular}}{\text{Base}}$$

​$$\tan 30\degree = \frac{1}{\sqrt3}$$​​

Solution:

​$$\tan(30^\circ) = \frac{40}{x}$$

x =$$\frac{40}{\tan(30^\circ)} = \frac{40}{\frac1{\sqrt{3}}} = 40\sqrt{3}$$​

Total distance = x + x $$= 2 \times 40\sqrt{3} = 80\sqrt{3}$$cm