Geometry

Trigonometry

Easy

The angle of elevation of the sun, when the length of the shadow of a tower is 1/√3 times the height of the tower, is

30°

45°

60°

90°

✅ Correct Option: 3

Let the height of the tower be $h$ .

The shadow length is $\frac{1}{\sqrt{3}} \times h = \frac{h}{\sqrt{3}}$ .

The tower, its shadow, and the line from the sun form a right-angled triangle where:

Height of tower (perpendicular) = $h$
Shadow length (base) = $\frac{h}{\sqrt{3}}$
Angle of elevation = $\theta$

Using the tangent ratio:

$\tan \theta = \frac{\text{Height}}{\text{Shadow}}$

$\tan \theta = \frac{h}{\frac{h}{\sqrt{3}}}$

$\tan \theta = h \times \frac{\sqrt{3}}{h}$

$\tan \theta = \sqrt{3}$

From standard trigonometric values, $\tan 60° = \sqrt{3}$ .

Therefore, $\theta = 60°$ .

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Solution

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