WAEC 2021 · Paper 2 · Q8✱✱

(a)
A boat sails $42\text{ km}$ from $M$ to $N$ on a bearing of $072^\circ$ , then to $P$ on a bearing of $342^\circ$ . $P$ is on a bearing of $038^\circ$ from $M$ . (i) Illustrate the information in a diagram. (ii) Calculate, correct to four significant figures: I. $|MP|$ ; II. $|NP|$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

At $N$ , the direction back to $M$ is $252^\circ$ and the direction to $P$ is $342^\circ$ , so $\angle MNP = 342^\circ - 252^\circ$
$= 90^\circ$ .
At $M$ , $\angle NMP = 72^\circ - 38^\circ$
$= 34^\circ$ .
I. $MP$ is the hypotenuse: $\cos 34^\circ = \frac{42}{|MP|}$ , so $|MP| = \frac{42}{0.8290} \approx 50.66$ km.
II. $\tan 34^\circ = \frac{|NP|}{42}$ , so $|NP| = 42 \times 0.6745 \approx 28.33$ km.