When the elevation of sunlight changes from 30° to 60°, the length of shadow of the pillar decreased by 15 m, find the height the pillar?
Answer & explanation
Correct answer: option 4
Let the height of the pillar = H
Tan 30° = \(\frac{AB}{P + 15}\)
\(\frac{1}{\sqrt {3}}\) = \(\frac{H}{P + 15}\)
(P + 15) = H\(\sqrt {3}\) ... (i)
and Tan 60° = \(\frac{AB}{BD}\) = \(\frac{H}{P}\)
H = P\(\sqrt {3}\) .... (ii)
From equation (i) and (ii)
\(\frac{P+15}{\sqrt {3}}\) = P\(\sqrt {3}\)
⇒ P + 15 = 3 P
⇒ 2 P = 15
⇒ P = 7.5 m
from equation (ii)
H = P\(\sqrt {3}\)
H = 7.5\(\sqrt {3}\)