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?

7.5\(\sqrt {3}\)

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\(\sqrt {3}\)