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 of the boy cast by the lamp ; (ii) angle of elevation of the lamp from the boy, correct to the nearest degree.
Explanation
(a)
(b) (tan theta = frac{4.2}{6 + x} ; tan theta = frac{1.2}{x})
(tan theta = tan theta)
(implies frac{4.2}{6 + x} = frac{1.2}{x})
(4.2 x = 1.2(6 + x) )
(4.2 x = 7.2 + 1.2 x implies 4.2x – 1.2x = 7.2)
(3x = 7.2 implies x = 2.4 m) (length of the shadow cast by the lamp)
(ii) (tan theta = frac{1.2}{2.4} = 0.5)
(theta = tan^{-1} (0.5) )
= (27°) (angle of elevation)