QJEEM19Ma7966: JEE Main 2019 Mathematics - Class 12 JEEM19Ma7966 Solution: Two vertical poles of heights, 20 m and 80 m stand a part on a…

From triangle BCD,

tan $\alpha$ = ${{80} \over x}$

and from triangle BFE,

tan $\alpha$ = ${{h} \over y}$

$\therefore$ ${{80} \over x}$ = ${{h} \over y}$

$\Rightarrow$ $y = {{hx} \over {80}}$ ........ (1)

From triangle ABC,

tan $\beta$ = ${{20} \over x}$

and from triangle EFC,

tan $\beta$ = ${{h} \over {x-y}}$

$\therefore$ ${{20} \over x}$ = ${{h} \over {x-y}}$

$\Rightarrow$ $x-y = {{hx} \over {20}}$ ........ (2)

By adding equation (1) and (2) we get,

x = ${{hx} \over {80}}$ + ${{hx} \over {20}}$

$\Rightarrow$ 1 = ${{h} \over {80}}$ + ${{h} \over {20}}$

$\Rightarrow$ h = 16 m

$\therefore$ Height of intersection point is 16 m