Question

What is the angle of elevation of a light source when the length of the shadow of a flagpost is equal to its height?

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

Answer 1

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

Let $AB$ be the height of the flagpost and $BC$ be the length of its shadow.

$AB=BC$ (given)

Let, the angle of elevation, $\angle ACB=\theta$

Now, in $△ACB$

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

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

$\Rightarrow \tan \theta =1$

$\Rightarrow \theta ={45}^{\circ }$

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