From a point $P$ on level ground, the angle of elevation of the top of a flagpole is $30^{\circ }$. If $P$ is $12\text{m}$ away from the base of the flagpole, calculate the height of the flagpole (rounded to two decimal places).

Step-by-step solution

1. Let the height of the flagpole be $h$ metres.
2. From the definition of tangent, $\tan 30^{\circ }=\frac{\text{opposite}}{\text{adjacent}}=\frac{h}{12}$.
3. Use the known value $\tan 30^{\circ }=\frac{1}{\sqrt{3}}\approx 0.577$.
4. Set up the equation: $0.577=\frac{h}{12}$.
5. Solve for $h$: $h=12\times 0.577=6.924$ metres.
6. Round to two decimal places: $h\approx 6.93\text{m}$.

Concept tested: Using tangent for height problems

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