Question

The moon's distance from the earth is $360000kms$ and its diameter subtends an angle of ${31}^{\prime }$ at the eye of the observer. Find the diameter of the moon.

• A. $3246.33kms$
• B. $3747.62kms$
• C. $3400.52kms$
• D. $3244.72kms$

Answer 1

The correct option is A $3246.33kms$

$AB=2d$

$PQ=36000$

$1^o={60}^{{}^{\prime }}$

$\Rightarrow \frac{\pi }{180}\Rightarrow {60}^{{}^{\prime }}$

$\Rightarrow 1^{{}^{\prime }}\to \frac{\pi }{180\times 60}$

$\therefore {31}^{{}^{\prime }}\to \frac{31\pi }{180\times 60}radius$

$△APQ\cong △PQB$

$\therefore LPQA=LPQB=\frac{31\pi }{180\times 120}$ radius

tan $\left(LPQA\right)=\frac{AP}{PQ}=\frac{d}{PQ}$

$\to 4.5088=\frac{d}{36\times {10}^4}$

$\to d=1623.168$

$\therefore$ diameter$2d=3246.33km$