Moon

We see the Moon from the perspective angle 28'. At the time of the full Moon, the Moon's radius is 1740 km. Calculate the mean distance of the Moon from the Earth.

Correct answer:

x =  425520 km

Step-by-step explanation:

$$\begin{gathered} r=1740\text{km} \\ u=28/60=\frac{7}{15}\doteq 0.4667{}^{\circ } \\ v=u/2=\frac{7}{15}/2=\frac{7}{15\cdot 2}=\frac{7}{30}\doteq 0.2333{}^{\circ } \\ w=\frac{\pi }{180}\cdot v=\frac{3.1416}{180}\cdot 0.2333\doteq 0.0041\text{rad} \\ \tan w=r/(x+r) \\ x=r/\tan w-r=1740/\tan 0.0041-1740=425520\text{km} \end{gathered}$$

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