Question

When the length of the shadow of a pole is equal to the height of the pole, the angle of elevation of the Sun has measure of ................

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${75}^o$

Answer 1

Answer: (B)

${45}^o$

Let $AB=h$ be the height of the pole.

The shadow of a pole will form base $BC$

Let $\theta$ be the angle of elevation.

According to the fig.
$\tan \theta =\frac{AB}{BC}$

$⟹\tan \theta =\frac{h}{h}=1$

$⟹\theta ={\tan }^{-1}\left(1\right)$

$⟹\theta ={45}^o$

Hence, the angle elevation is ${45}^o$.