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°?
Answer & explanation
Correct answer: option 3
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