JAMB 2010 · UTME · Q38

If $\cot\theta = \frac{8}{15}$ , where $\theta$ is acute, find $\sin\theta$ .

Worked solution (try it first)

$\cot\theta = \frac{\text{adjacent}}{\text{opposite}}$
$= \frac{8}{15}$ , so draw a right-angled triangle with adjacent side 8 and opposite side 15.
Pythagoras: the hypotenuse is $\sqrt{64 + 225} = \sqrt{289} = 17$ .
So $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$
$= \frac{15}{17}$ , option B.