Answer to Question #6716 in Geometry for Arzo

Question

hello, could you help me with this one: If you look at a coin from 2.8 meter, it looks as big as a full moon. The dictance between the moon and earth is 384000 km (swedish km). The coin got a diameter at 25 mm. Count the moons diameter.

Answer 1

Let α be the angle of view. We know that

tg(α/2) = (0.25/2)/2.8 = 5/112.

From the other side,

tg(α/2) = (D/2)/384000,

where D is the moon's diameter. So,

(D/2)/384000 = 5/112 ==> D = 5/112*384000*2 = 240000/7 km.