Question

If the height of a pole is \( 2\sqrt{3} \) metres and the length of its shadow is 2 metres, what is the angle of elevation of the sun?

• A. \( 60^\circ \)
• B. \( 45^\circ \)
• C. \( 30^\circ \)
• D. \( 15^\circ \)

Hint:

Use \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\) when height and shadow length are given to find angle of elevation.

Answer 1

The Correct Option is A

Step 1: Use the definition of tangent in a right triangle.
Let \( \theta \) be the angle of elevation of the sun. We have: \[ \tan(\theta) = \frac{\text{Height of pole}}{\text{Length of shadow}} = \frac{2\sqrt{3}}{2} = \sqrt{3} \] Step 2: Use trigonometric value.
We know that: \[ \tan(60^\circ) = \sqrt{3} \] So, \( \theta = 60^\circ \)