WAEC 2021 · Paper 1 · Q19

In $\triangle LMN$ , $|LM| = 6\text{ cm}$ , $\angle LNM = x$ , angle $L$ is a right angle and $\sin x = \frac35$ . Find the area of $\triangle LMN$ .

Worked solution (try it first)

The right angle is at $L$ , so $MN$ is the hypotenuse and $LM = 6$ is the side opposite the angle $x$ at $N$ : $\sin x = \dfrac{6}{MN} = \dfrac35$ .
So $MN = 10$ cm, and Pythagoras gives $LN = \sqrt{10^2 - 6^2} = 8$ cm.
The two sides at the right angle are the base and height: area $= \frac12 \times 6 \times 8$
$= 24\text{ cm}^2$ , option C.