The shadow of a streetlight is 54 m when the elevation of sun is 30°. What is the length of the shadow when sun's elevation becomes 60°?

18 m

tan θ = \(\frac{height\;of\;street\;light}{shadow's\;length}\)

height of street light is constant

Therefore, Ratio of tan θ ∝ \(\frac{1}{length\;of\;shadow}\)

Ratio of tan θ ⇒

tan 30°        :        tan 60°

\(\frac{1}{\sqrt {3}}\)             :        \(\sqrt {3}\)  = 1 : 3

Ratio of length of shadow   3     :      1

                                            ↓            ↓

                                54 (given)      × 18 = 18 m