WAEC 2014 · Paper 2 · Q10

(a)
(i) Solve the inequality $\frac12x - \frac56(x + 2) \le 1 + x$ . (ii) Illustrate the solution on a number line.
Model answer
(i) $x \ge -2$ . (ii) A solid dot at $-2$ (it is included) with an arrow to the right.
(b)
From a point $P$ on level ground and directly west of a pole, the angle of elevation of the top of the pole is $45^\circ$ , and from a point $Q$ east of the pole, the angle of elevation of the top of the pole is $58^\circ$ . If $|PQ| = 10\text{ m}$ , calculate, correct to 2 significant figures, the: (i) distance from $P$ to the pole; (ii) height of the pole.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

On a number line, put a solid dot at $-2$ (because $-2$ is included) and an arrow pointing to the right.

The pole stands between $P$ (to the west) and $Q$ (to the east).
Let the distance from $P$ to the foot of the pole be $x$ m.
Then $Q$ is $(10 - x)$ m from it.
The height $h$ from each side: $h = x\tan 45^\circ = x$ , and $h = (10 - x)\tan 58^\circ$ .
Set them equal: $x = (10 - x)(1.6003)$ .
So $x + 1.6003x = 16.003$ , $2.6003x = 16.003$ and $x \approx 6.154$ .