Find the angle of elevation of the Sun, when the length of the shadow of a tree is \(\frac{1}{\sqrt{3}}\) times the height of the tree.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 60°
The angle of elevation of the Sun is the angle that the Sun’s ray makes with the ground at the tip of the shadow. The tree, its shadow and the ray form a right-angled triangle, in which tan of the angle = height of the tree ÷ length of the shadow.
Height \(=h\), shadow \(\displaystyle=\frac{h}{\sqrt{3}}\)
From the triangle: \(\displaystyle\tan\theta=h\div\frac{h}{\sqrt{3}}=\sqrt{3}\)
The angle whose tangent is \(\sqrt{3}\) is \(60^\circ\), so \(\theta=60^\circ\)
