In a right‑angled triangle, the angle at the base is $35^{\circ }$ and the side opposite this angle is $15\text{m}$. Find the length of the hypotenuse.

Step-by-step solution

1. Label the triangle: opposite side = 15 m, angle $\theta =35^{\circ }$, hypotenuse = $c$.
2. Use the sine relation $\sin \theta =\frac{\text{opposite}}{\text{hypotenuse}}$, i.e. $\sin 35^{\circ }=\frac{15}{c}$.
3. Rearrange to $c=\frac{15}{\sin 35^{\circ }}$.
4. Calculate $\sin 35^{\circ }\approx 0.574$, therefore $c\approx \frac{15}{0.574}=26.13\text{m}$.
5. Round to one decimal place: $c\approx 26.1\text{m}$.

Concept tested: Finding hypotenuse (trigonometric ratios)

Published 22 August 2026 · How this solution was prepared and checked

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