If the length of the shadow of a tower is \(\sqrt{3}\) times its height, then the angle of elevation of the sun is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 30°
The tower, its shadow and the sun’s ray form a right-angled triangle. The angle of elevation of the sun is the angle at the tip of the shadow, and its tangent is height ÷ shadow (the side opposite the angle over the side next to it).
Let the height of the tower be \(h\); the shadow is then \(\sqrt{3}\,h\)
Tangent of the angle of elevation: \(\displaystyle\tan\theta=\frac{h}{\sqrt{3}\,h}=\frac{1}{\sqrt{3}}\)
The angle whose tangent is \(\frac{1}{\sqrt{3}}\) is \(30^{\circ}\), so \(\theta=30^{\circ}\)
