Moon

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

Correct answer:

x =  425520 km

Step-by-step explanation:

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

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