Question

Kurukshetra is $64\, km$ from Ambala. Find to the $30$. nearest second the angle subtended at the centre of the earth by the arc joining these two towns, the earth being regarded as a sphere of radius $6400\, km$.

• A. $34'22''$ nearly
• B. $40'20''$ nearly
• C. $32'20''$ nearly
• D. None of these

Answer 1

Answer: (A)

$34'22''$ nearly

Answer 2

Let $O$ be the centre of the earth. Let $K$ and $A$ be the positions of Kurukshetra and Ambala. Here $l =$ arc $KA = 64\, km$ $r =$ radius of earth $= 6400 \,km$ If $\theta$ radians be the angle $AOK$. Then, $\theta=\frac{l}{r}=\frac{64}{6400}=\frac{1}{100}$ $\therefore \angle AOK=\frac{1}{100}$ radian $=\frac{1}{100}\times\frac{180^{\circ}}{\pi}$ $=\frac{9^{\circ}}{5\pi}=\frac{9^{\circ}}{5}\times\frac{7}{22}=\frac{63^{\circ}}{110}=\frac{63}{110}\times 60'$ $=34'\,22''$ nearly