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.

Result

x =  425520 km

Solution:

r=1740 km u=28/60=715≐0.4667 ∘  v=u/2=0.4667/2≐730≐0.2333 ∘  w=π180⋅ v=3.1416180⋅ 0.2333≐0.0041 rad  tan⁡(w)=r/(x+r)  x=r/tan⁡(w)−r=1740/tan⁡(0.0041)−1740≐425520.4509≐425520 kmr=1740 \ \text{km} \ \\ u=28/60=\dfrac{ 7 }{ 15 } \doteq 0.4667 \ ^\circ \ \\ \ \\ v=u/2=0.4667/2 \doteq \dfrac{ 7 }{ 30 } \doteq 0.2333 \ ^\circ \ \\ \ \\ w=\dfrac{ \pi }{ 180 } \cdot \ v=\dfrac{ 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 \doteq 425520.4509 \doteq 425520 \ \text{km}

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