Question

The angle of elevation of the sun, when the length of the shadow of a pole is equal to its height, is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

Let the height of the pole be $AB=xm$

Then the length of the shadow of the pole $AB$ will be $OB=xm$

Let the angle of elevation be $\theta$ i.e., $\angle AOB=\theta$

In the right-angled triangle $OAB,$ we have

$\Rightarrow \tan \theta =\frac{AB}{OB}$

$=\frac{x}{x}$

$=1$

$\Rightarrow \theta ={\tan }^{-1}{45}^{\circ }$

Therefore angle of elevation is ${45}^{\circ }$