Question

two poles of equal heights are standing opposite each other on either side of the road,which is 80 m wide. From a point between them on the road, the angles of elevation ofthe top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.​

Answer 1

$\huge {\bold {HOLA....!!}}$

$<b><font >$

Let AC and BD be the two poles of same height 'h' m.

Given AB = 80 m

Let AP = x m, therefore, PB = (80 - x) m

In ▶️APC,

$tan {30}^{°} = \frac{AC}{AP} \\ \\ \frac{1}{ \sqrt{3 } } =\frac{h}{x} \: \: \: ..... (1)$

In▶️ BPD,

$tan {60}^{°} =\frac{BD}{AB}\\ \\ \sqrt{3 }=\frac{h}{80-x} \: \: \: ..... (2)$

$Dividing \:(1) \:by\: (2),$

$=>\frac{\frac{1 } {\sqrt{3 }} } {\sqrt{3 }} =\frac{\frac{h} {x} } {\frac{h} {80-x}} \\ \\ => \frac {1}{3} =\frac {80-x}{x} \\ \\ =>x = 240 - 3x\\ \\ =>4x = 240 \\ \\ =>x =\frac {240}{4} \\ \\ =>x=60\\ \\ from \: (1), \\ \\ \frac{1 }{\sqrt{3 }} =\frac{h}{x}\\ \\ =>h = \frac {60} {\sqrt{3 }} \\ \\ =>20\sqrt{3 }m$

Thus, the height of both the poles is $20\sqrt{3 }$ m and the distances of the point from the poles are 60 m and 20 m.

$</b ></font >$

$\huge {\bold{Hope\:It \:Helps }}$

Answer 2

Answer:

Refer to the attachment for ur answer dear..