Question

What is the angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree?

• A. ${60}^{\circ }$
• B. ${45}^{\circ }$
• C. ${80}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B

${45}^{\circ }$

Consider the diagram shown above where QR represents the tree and PQ represents its shadow.
We have, $QR=PQ$ (Given)
Let $\angle QPR=\theta$.
$\tan \theta =\frac{QR}{PQ}=1$ $\because QR=PQ$
$\Rightarrow \theta ={45}^{\circ }$
i.e., required angle of elevation = ${45}^{\circ }$