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)