A boy 1.2m tall, stands 6m away from the foot of a vertical lamp pole...

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)