Question

The moon is observed from two diametrically opposite points $A$ and $B$ on earth. The angle $\theta$ subtended at the moon by the two directions of observation is $1^0{54}^{\prime }$. Given the diameter of the earth to be about $1.276\times {10}^{7}m$, compute the distance of the moon from the earth.

Answer 1

From figure,

$AB=l\theta ,$ where $\theta$ in rodians

$\therefore l=\frac{AB}{\theta }$

$⟹\frac{1.276\times {10}^7}{0.03316}$

$⟹3.848\times {10}^{8}m$

Since $l$ is large,$l\approx CD=3.848\times {10}^{8}m$