Question

Two poles of equal heights two poles of equal height are standing opposite to each other on either side of the road which is 80m wide from a point in between them on the road the angles of elevation of the top of poles are 60 degree and 30 degree respectively. Find the height of the poles and the distance of the point from the point​

Answer 1

Answer:

here is the solution

sorry it's in bad writing please try to understand or another wise ask me again to write

Answer 2

Two poles of equal heights are standing opposite each other on either side of the road = 80m

Angles of elevation of the top of the poles = 60° & 30°

$\large\tt\red{In\:∆ABC,}$

$\longrightarrow$$\large\tt\purple{tan\:60°=\frac{AB}{BC}}$

$\longrightarrow$$\large\tt\purple{√3=\frac{h}{x}}$

$\longrightarrow$$\large\tt\purple{h=√3x}$.....(1)

$\large\tt\red{In\:∆DEC,}$

$\longrightarrow$$\large\tt\purple{tan\:30°=\frac{DE}{CE}}$

$\longrightarrow$$\large\tt\purple{\frac{1}{√3}=\frac{h}{80-x}}$......(2)

$\large\tt\green{Put\:h=√3x\:in\:equation(2)}$

$\longrightarrow$$\large\tt\purple{\frac{1}{ \sqrt{3} } = \frac{ \sqrt{3} }{80 - x} }$

$\longrightarrow$$\large\tt\purple{3x-80-x}$

$\longrightarrow$$\large\tt\purple{3x+x=80}$

$\longrightarrow$$\large\tt\purple{3x+x=80}$

$\longrightarrow$$\large\tt\purple{4x=80}$

$\longrightarrow$$\large\tt\purple{x=20m}$

$\longrightarrow$$\large\tt\pink{h=√3x}$

$\longrightarrow$$\large\tt\pink{h=√3×20}$

$\longrightarrow$$\large\tt\pink{h=20√3m}$