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 $1^{\circ} 54^{\prime}$. Given the diameter of the Earth to be about $1.276 \times 10^{7} \; m$,compute the distance of the moon from the Earth.

(D) Given: The angle $\theta = 1^{\circ} 54^{\prime} = 60^{\prime} + 54^{\prime} = 114^{\prime}$.
To convert $\theta$ into radians,we use the relation $1^{\prime} = 2.91 \times 10^{-4} \; rad$.
So,$\theta = 114 \times 2.91 \times 10^{-4} \; rad \approx 3.32 \times 10^{-2} \; rad$.
The diameter of the Earth $b = 1.276 \times 10^{7} \; m$.
Using the parallax formula $D = b / \theta$,where $D$ is the distance of the moon from the Earth:
$D = \frac{1.276 \times 10^{7}}{3.32 \times 10^{-2}} \; m$.
$D \approx 3.84 \times 10^{8} \; m$.