The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 45°
The tree, its shadow and the Sun’s ray form a right-angled triangle, and the angle of elevation \(\theta\) of the Sun is at the tip of the shadow, with \(\tan\theta=\frac{\text{height of the tree}}{\text{length of the shadow}}\).
Shadow \(=\) height \(=h\), so \(\tan\theta=\frac{h}{h}=1\)
\(\tan45^\circ=1\), so \(\theta=45^\circ\)