A 1.2 metre tall boy stands vertically at 5 pm when the sun’s altitude is 30°. What is the length of his shadow, rounded to two decimal places?

Step-by-step solution

1. Draw a right‑angled triangle with the boy’s height as the opposite side and the shadow as the adjacent side.
2. Recognise that the angle of elevation of the sun is 30°, which is also the angle of the triangle.
3. Use the relation $\tan 30°=\frac{\text{opposite}}{\text{adjacent}}$. So $\text{shadow}=\frac{\text{height}}{\tan 30°}$.
4. Calculate $\tan 30°=\frac{\sqrt{3}}{3}\approx 0.577$.
5. Compute $\frac{1.2}{0.577}\approx 2.078$ metres.
6. Round to two decimal places: $2.08$ metres.

Concept tested: Shadow length using trigonometry

Published 4 October 2026 · How this solution was prepared and checked