Question

If a flag of 6 meters height, placed on top of a tower, throws a shadow of \( 2\sqrt{3} \) meters along the ground, then the angle in degrees that the sun makes with the ground is

• A. 30°
• B. 45°
• C. 60°
• D. 75°

Hint:

To find the angle of elevation, use the tangent function \( \tan(\theta) = \frac{\text{height}}{\text{length of shadow}} \).

Answer 1

The Correct Option is C

We are given that the height of the flag (opposite side) is 6 meters, and the length of the shadow (adjacent side) is \( 2\sqrt{3} \) meters. The angle of elevation \( \theta \) can be found using the tangent function: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{6}{2\sqrt{3}} = \frac{3}{\sqrt{3}} = \sqrt{3}. \] Thus, \( \theta = 60^\circ \), as \( \tan(60^\circ) = \sqrt{3} \).