The angle of elevation of the top of a mountain from the top of the house is 30°. The distance (shortest) between top of the house and top of the mountain is 13\(\sqrt {3}\) m.  If height of house is 5.196 m then find the height of the mountain.

\(\frac{19\sqrt {3}}{2}\)

AE = Mountain

BD = House

In ΔABC:

⇒ Sin 30° = \(\frac{Perp.}{Hyp.}\) = \(\frac{AC}{AB}\)

⇒ \(\frac{1}{2}\) = \(\frac{AC}{13\sqrt {3}}\)

⇒ AC = \(\frac{13\sqrt {3}}{2}\)

Here,

BD = CE = 5.196 m = 3 × 1.732 = 3\(\sqrt {3}\)

Height of Mountain (AE) = AC + CE = \(\frac{13\sqrt {3}}{2}\) + 3\(\sqrt {3}\) = \(\frac{19\sqrt {3}}{2}\)