Question

The moon is observed from two diametrically opposite points on earth. The angle subtended at the moon by the two directions of observations is $1^o{54}^{\prime }$. Given the diameter of the earth to be about $2.276\times {10}^{7}m$, compute the distance of moon from the earth.

• A. $1\times {10}^{8}m$
• B. $6.84\times {10}^{8}m$
• C. $6.84\times {10}^{10}m$
• D. $38.4\times {10}^{8}m$

Answer 1

The correct option is B $6.84\times {10}^{8}m$

Here D be the distance between the moon and the earth, d be the diameter of the earth.

Here, $\theta =1^o{54}^{\prime }={1.9}^o=\frac{\pi }{180}\times 1.9rad=0.033$ radian

From the figure, $\tan \theta =d/D$

As $\theta$ is very small, $\theta =d/D$

$D=\frac{d}{\theta }=\frac{2.276\times {10}^7}{0.033}=6.84\times {10}^8$ m