From a point on the ground, the angle of elevation of the top of a telephone pole is $30^{\circ }$. If the horizontal distance from the point to the foot of the pole is $10\sqrt{3}\text{m}$, what is the height of the pole?

Step-by-step solution

1. Draw a right triangle with the pole as the vertical side and the given distance as the base.
2. Use the definition of tangent: $\tan 30^{\circ }=\frac{\text{height}}{10\sqrt{3}}$.
3. Since $\tan 30^{\circ }=\frac{1}{\sqrt{3}}$, set $\frac{1}{\sqrt{3}}=\frac{h}{10\sqrt{3}}$.
4. Cross‑multiply to get $h=10$ metres.
5. Thus the pole is $10\text{ m}$ tall.

Concept tested: Height from angle of elevation

Published 20 August 2026 · How this solution was prepared and checked