WAEC 2022 · Paper 2 · Q5

(a)
A bird perches on the top of a slanted tree of length $12.8\text{ m}$ . If the bird is $10\text{ m}$ vertically above the ground, (i) illustrate the information in a diagram; (ii) find, correct to the nearest degree, the angle of depression of the foot of the tree from the bird.
(b)

Marks 1 2 3 4 5 6 7 8 9

Number of students 11 12 10 17 16 15 14 13 12

The table shows the distribution of marks obtained by some students in a test. If a student is selected at random from the class, find the probability that the student obtained at most 7 marks.

Marks	1	2	3	4	5	6	7	8	9
Number of students	11	12	10	17	16	15	14	13	12

Worked solution (try it first)

Draw the slanted tree as the hypotenuse, 12.8 m, from its foot on the ground to the bird at the top, which is 10 m vertically above the ground.

The angle of depression from the bird equals the angle of elevation of the bird from the foot of the tree (alternate angles).
The 10 m height is opposite that angle and the tree is the hypotenuse: $\sin\theta = \frac{10}{12.8}$
$\approx 0.7813$ , so $\theta \approx 51.4^\circ$
$\approx 51^\circ$ .

Total number of students: $11 + 12 + 10 + 17 + 16 + 15 + 14 + 13 + 12 = 120$ . "At most 7 marks" means 7 marks or fewer, so leave out those who scored 8 or 9: $120 - (13 + 12) = 95$ .
Probability $= \frac{95}{120} = \frac{19}{24}$ .