JEE PYQ: Heights And Distances Question 14
Question 14 - 2019 (10 Jan Shift 1)
Consider a triangular plot ABC with sides $AB = 7$ m, $BC = 5$ m and $CA = 6$ m. A vertical lamp-post at the mid point D of AC subtends an angle $30°$ at B. The height (in m) of the lamp-post is:
(1) $\frac{3}{2}\sqrt{21}$ (2) $\frac{2}{3}\sqrt{21}$ (3) $2\sqrt{21}$ (4) $7\sqrt{3}$
Show Answer
Answer: (2) $\frac{2}{3}\sqrt{21}$
Solution
By Apollonius: $BD = 2\sqrt{7}$. $h = \frac{2\sqrt{7}}{\sqrt{3}} = \frac{2\sqrt{21}}{3}$.
BETA
