Question

If the ratio of the length of a pole and its shadow is \(1:\sqrt3\), then the angle of elevation of the sun is 

• A. 30°
• B. 45°
• C. 60°
• D. 90°

Answer 1

The Correct Option is C

Let the length of the pole be \( h \) and the length of the shadow be \( x \). Given, the ratio of the length of the pole to the length of the shadow is: \[ \frac{h}{x} = \frac{1}{\sqrt{3}} \] This means that the height of the pole is \( 1 \) and the length of the shadow is \( \sqrt{3} \). In a right-angled triangle formed by the pole, its shadow, and the line from the top of the pole to the tip of the shadow, the tangent of the angle of elevation \( \theta \) of the sun is given by: \[ \tan \theta = \frac{\text{height of the pole}}{\text{length of the shadow}} = \frac{1}{\sqrt{3}} \] We know that: \[ \tan 60° = \sqrt{3} \] Thus, the angle of elevation \( \theta \) is \( 60° \).

The correct option is (C): \(60°\)