NECO 2023 · Paper 1 · Q46

If $\cos\theta = 0.8$ and $0^\circ < \theta < 90^\circ$ , find $\tan\theta$ .

Worked solution (try it first)

$\cos\theta = 0.8 = \frac45$ , so draw a right-angled triangle with adjacent side 4 and hypotenuse 5.
Pythagoras gives the opposite side: $\sqrt{25 - 16} = 3$ .
So $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$
$= \frac34$ , option B.