Question

Length of the shadow of 15 m tall building is 15 m at 1 pm. What is the angle of elevation of the sun's rays with the ground at the time?

• A. 30°
• B. 60°
• C. 45°
• D. 90°

Answer 1

The correct option is C 45°

The given scenario form a right-angled triangle, where perpendicular is the height of the building, that is, 15 m, and the shadow length is the base of the right angle triangle.

$\therefore \tan \theta =\frac{\text{Perpendicular}}{\text{Base}}$

Substitute 15 for "Perpendicular" and 15 for "Base" into the above relation to find the elevation angle.
$\begin{array}{cc}\tan \theta & =\frac{\text{15}}{\text{15}}\\ & =1\\ \theta & ={\tan }^{-1}\left(1\right)\\ & ={45}^{\circ }\end{array}$

Hence, the angle of elevation is ${45}^{\circ }$.