JAMB 1997 · UME · Q36

In a triangle $XYZ$ , if $\angle XYZ = 60^\circ$ , $XY = 3$ cm and $YZ = 4$ cm, calculate the length of the side $XZ$ .

Worked solution (try it first)

You have two sides and the angle between them, so use the cosine rule: $XZ^2 = 3^2 + 4^2 - 2(3)(4)\cos60^\circ$ .
$\cos60^\circ = \frac12$ , so the last term is $24 \times \frac12 = 12$ and $XZ^2 = 25 - 12 = 13$ .
So $XZ = \sqrt{13}$ cm, option B.