WAEC 2013 · Paper 2 · Q5

(a)
A boy $1.2\text{ m}$ tall stands $6\text{ m}$ away from the foot of a vertical lamp pole $4.2\text{ m}$ high. If the lamp is at the tip of the pole, (i) represent this information in a diagram; (ii) calculate the length of the shadow of the boy cast by the lamp; (iii) calculate the angle of elevation of the lamp from the boy, correct to the nearest degree.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)(i)

Draw the lamp pole (4.2 m) and the boy (1.2 m) upright on the ground, 6 m apart.
The light from the lamp just passes the top of the boy's head and reaches the ground at the end of his shadow.

(ii)

Let the shadow be $y$ m long.
The boy and the pole make two similar right-angled triangles with the tip of the shadow: $\frac{y}{1.2} = \frac{y + 6}{4.2}$ .
Cross-multiply: $4.2y = 1.2y + 7.2$ .
So $3y = 7.2$ and $y = 2.4\text{ m}$ .

(iii)

From the top of the boy's head, the lamp is $4.2 - 1.2 = 3$ m higher and 6 m away horizontally: $\tan\theta = \frac36 = 0.5$ .
So $\theta \approx 26.6^\circ$
$\approx 27^\circ$ .

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