Question

5. A boy 1.2m tall, stands 6m away from the foot of a vertical lamp pole 4.2m long. If the lamp is at the tip of the pole:
(a) represent this information in a diagram;
(b) calculate the: (i) length of the shadow cast by the boy; (ii) angle of elevation of the lamp from the boy, correct to the nearest degree.

Accepted Answer

(a) The diagram shows a vertical lamp pole of height 4.2m with the lamp at the top, a boy of height 1.2m standing 6m from the foot of the pole, and a light ray from the lamp grazing the boy's head to cast a shadow on the ground.

(b)(i) Using similar triangles: let x = length of the boy's shadow. By similar triangles, (4.2)/(6+x) = (1.2)/x. Cross-multiplying: 4.2x = 1.2(6+x) = 7.2+1.2x. So 3x = 7.2, x = 2.4m. Length of shadow cast by the boy = 2.4m.
(ii) The angle of elevation θ of the lamp from the boy: tanθ = (4.2−1.2)/6 = 3/6 = 0.5. θ = tan⁻¹0.5 = 26.57° ≈ 27° (nearest degree).

WAEC Mathematics 2012 Theory — Question 5

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