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.
Answer & explanation
Correct answer: option 4
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\(\sqrt {3}\) = \(\frac{19\sqrt {3}}{2}\)