Question

I honestly have NO idea how I am supposed to work this information

Let's shoot a laser, at a reflector on the moon. What diameter would the reflector have to be to capture the entire beam? distance to moon = 250,000 miles = 400,000 km = 4x10^10 cm.

Answer 1

Angular size = Diameter of reflector / Distance to moon

$\theta=\frac{D}{X}$

$D=\theta X$

Beam angle $\theta =8\degree=8*\frac{\pi}{180} \,rad$

Distance from earth to moon $X=4*10^{5}\,km=4*10^8\,m$

$D=\theta X=8*\frac{\pi}{180}*4*10^8=5.58*10^7\,m=5.58*10^4\,km$

Diameter of reflector must be $D=5.58*10^7\,m=5.58*10^4\,km$