WAEC 2021 · Paper 2 · Q12

(a)
The angle of depression of a boat from the midpoint of a vertical cliff is $35^\circ$ . If the boat is $120\text{ m}$ away from the foot of the cliff, calculate, correct to one decimal place, the height of the cliff.
(b)
Using the quadratic formula, solve, correct to three significant figures, $2x^2 + 3x - 4 = 0$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

Draw the cliff with its midpoint $M$ halfway up, and the boat 120 m from the foot.
The angle of depression from $M$ equals the angle of elevation of $M$ from the boat, $35^\circ$ .
So half the height is $120\tan 35^\circ \approx 84.02$ m, and the cliff is $2 \times 84.02 \approx 168.0$ m high.

(b)

With $a = 2$ , $b = 3$ , $c = -4$ : $x = \frac{-3 \pm \sqrt{9 + 32}}{4}$
$= \frac{-3 \pm \sqrt{41}}{4}$
$= \frac{-3 \pm 6.403}{4}$ .
So $x \approx 0.851$ or $x \approx -2.35$ (3 significant figures).

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