Question

Find the angle of elevation of the Sun when the length of the shadow of a pole is $\sqrt{3$ times the height of the pole.}

• A. 30°
• B. 45°
• C. 60°
• D. 90°

Hint:

Use right triangle trigonometry: angle of elevation $\theta$ satisfies $\tan \theta = \frac{\text{height}}{\text{shadow length}}$.

Answer 1

The Correct Option is A

Let the height of the pole be $h$ and the length of its shadow be $s = \sqrt{3}h$. Let $\theta$ be the angle of elevation of the Sun. From right triangle formed by the pole and its shadow, \[ \tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{\sqrt{3}h} = \frac{1}{\sqrt{3}} \] Using the standard trigonometric values, \[ \tan 30° = \frac{1}{\sqrt{3}} \implies \theta = 30° \]