Mathematics — Standard (041) — CBSE Class 10 board question

Let the height of the tower be $h$ and the length of its shadow be $\sqrt{3}\,h$.

Let $\theta$ be the angle of elevation of the sun.

In the right triangle formed:

$$\tan\theta = \frac{\text{height of tower}}{\text{length of shadow}} = \frac{h}{\sqrt{3}\,h} = \frac{1}{\sqrt{3}}$$

Since $\tan 30° = \dfrac{1}{\sqrt{3}}$, we get $\theta = 30°$.

The angle of elevation of the sun is 30°.

Source: Chapter 9, Heights and Distances (Exercise 9.1)

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• Draw the right triangle with the tower as the perpendicular side and the shadow as the base.
• Use $\tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{\sqrt{3}h}$; the $h$ cancels, leaving $\frac{1}{\sqrt{3}}$.
• Recall the standard value: $\tan 30° = \frac{1}{\sqrt{3}}$, so $\theta = 30°$.
• Always state the final answer clearly; examiners award the last mark for the correct conclusion.