WAEC 2019 · Paper 2 · Q8

(a)
Solve the inequality $\frac13x - \frac14(x + 2) \ge 3x - 1\frac13$ .
Show the answer
$x \le \frac27$
(b)
In the diagram, $ABC$ is a right-angled triangle on a horizontal ground and $|AD|$ is a vertical tower. $\angle BAC = 90^\circ$ , $\angle ACB = 35^\circ$ , $\angle ABD = 52^\circ$ and $|BC| = 66\text{ m}$ . Find, correct to two decimal places, the: (i) height of the tower; (ii) angle of elevation of the top of the tower from $C$ .
A 3-D sketch: triangle ABC lies on the ground and AD is vertical.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

In triangle $ABC$ the right angle is at $A$ , so $BC = 66$ m is the hypotenuse.
$AB$ is opposite the $35^\circ$ angle at $C$ : $|AB| = 66\sin 35^\circ \approx 37.86$ m.
The tower $AD$ stands at $A$ , and from $B$ its top is at $52^\circ$ : $|AD| = |AB|\tan 52^\circ$
$\approx 37.86 \times 1.2799$
$\approx 48.45$ m.

$|AC| = 66\cos 35^\circ \approx 54.06$ m.
From $C$ : $\tan\theta = \frac{48.45}{54.06}$
$\approx 0.8962$ , so $\theta \approx 41.87^\circ$ .