Question

A pole of height h stands at one corner of a park in the shape of an equilateral triangle. If
$\alpha$
is the

angle which the pole subtends at the midpoint of the opposite side, the length of each side of the

park is​

Answer 1

EXPLAINED CLEARLY IN THE PICTURE

HOPE IT HELPS....

PLS MARK AS BRAINLIEST

Answer 2

The  length of each side of the  park is​ $\frac{2}{\sqrt{3}}h\cot\alpha$

Step-by-step explanation:

in triangle PBD

$\tan \alpha = \frac{h}{BD}\\\\BD = \frac{h}{\tan \alpha}\\\\BD = h \cot\alpha ...(1)$

now , in triangle BCD

$\angle DCB = 60^\circ \\\\\angle BDC = 180- (60+30) = 90^\circ$

thus , in triangle BCD

$\cos 30^\circ = \frac{BD}{BC}\\\\\frac{\sqrt{3}}{2}= \frac{h\cot\alpha}{BC}\\\\BC= \frac{2}{\sqrt{3}}h\cot\alpha$

hence , The  length of each side of the  park is​ $\frac{2}{\sqrt{3}}h\cot\alpha$

#Learn more :

https://brainly.in/question/7488696