Answer to Question #277175 in Optics for Malia

Question

Given that the moon has about has the same angular size as the new 20 peso coin, held at 1m from the eye and that the diameter of the moon is 3.5 x 10^6 m estimate the distance from the earth to the moon.

Answer 1

Let the diameter of the coin be $D=32\ mm=0.032\ m$ .

$\tan\alpha=\frac{D/2}{l}=\frac{D_M/2}{L}\to L=D_M\cdot l/D=3.5\cdot10^6\cdot1/0.032=109\ 000\ 000\ (m)$

In reality $L=384\ 400\ 000\ (m)$ .

Very inaccurate approximation.