WAEC 2016 · Paper 2 · Q4

(a)
Solve the inequality $\frac23(1 - 4x) - \frac12(5 - 3x) \le \frac14(7 + 9x) - \frac13$ .
Show the answer
$x \ge -\frac{39}{41}$
(b)
A man standing $3\text{ m}$ away from a tree observed that the angle of elevation of the top of the tree and the angle of depression of the bottom of the tree are $65^\circ$ and $20^\circ$ respectively. Find, correct to 3 significant figures, the height of the tree.

Worked solution (try it first)

(a)

Multiply every term by 12: $8(1 - 4x) - 6(5 - 3x) \le 3(7 + 9x) - 4$ .
Expand: $8 - 32x - 30 + 18x \le 21 + 27x - 4$ .
So $-22 - 14x \le 17 + 27x$ .
Collect terms: $-39 \le 41x$ , so $x \ge -\frac{39}{41}$ .

(b)

The man's eye is level with some point on the tree.
Up from his eye level to the top: $3\tan 65^\circ \approx 6.434$ m.
Down from his eye level to the bottom: $3\tan 20^\circ \approx 1.092$ m.
The tree's height is the sum: $6.434 + 1.092 \approx 7.53\text{ m}$ .

Report a problem with this question