Question

एक मीनार की चोटी से 7 मीटर ऊंचे भवन के शिखर और आधार के अवनमन कोण क्रमशः 45 डिग्री और 60 डिग्री है मीनार की ऊंचाई ज्ञात कीजिए

Answer 1

i hope apko samjh aayga .........

Answer 2

Height = $\frac{21 - 7\sqrt{3} }{2}$

Step-by-step explanation:

I have attached the question figure drawn by me in this answer.

Let h be the height of the minar and b be the distance between the bases of the house and the minar.

So, $\frac{h}{b}$ = tan 60°

     b = $\frac{h}{\sqrt{3} }$

Now as shown in the figure,

$\frac{x}{b}$ = tan 45°

so x = b

Also, x + h = 7                (Height of house is 7m)

  b + h = 7

  $\frac{h}{\sqrt{3} }$ + h = 7

 h(1 + $\frac{1}{\sqrt{3} }$) = 7

 h($\frac{\sqrt{3} + 1 }{\sqrt{3} }$) = 7

 h = $\frac{7\sqrt{3} }{\sqrt{3} + 1 }$

now rationalising

h = $\frac{21 - 7\sqrt{3} }{2}$