Question

If the height of a pole is 2 meters and the length of its shadow is 2 meters, find the angle of elevation of the sun.

• A. 30
• B. 90
• C. 180
• D. 60
• E. 45

Hint:

To find the angle of elevation, use the formula \( \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} \) and then find \( \theta \).

Answer 1

Answer: (E)

Step 1: Use the trigonometric formula for the tangent of an angle in a right triangle: \[ \tan \theta = \frac{\text{Height}}{\text{Shadow length}}. \] Step 2: Substituting the values: \[ \tan \theta = \frac{2}{2} = 1. \] Step 3: Find the angle whose tangent is 1: \[ \theta = \tan^{-1}(1) = 45^\circ. \] Thus, the angle of elevation is \( 45^\circ \).