Solid Angle of Moon: How Far for Dime to Appear Same Size?

[AnthonyS]

Homework Statement

How many inches from your face would you have to hold a dime in order for it to appear the exact same size as the Moon? Use a distance to the Moon of 384,400 km and a radius of the Moon of 1738 km. The diameter of a dime is 17.1 mm. (Hint: Find at what distance a dime has the same solid angle as the Moon).

Homework Equations

dω = sin θ dθ dφ

The Attempt at a Solution

This is for my Physics of Meteorology class. I am trying to find the solid angle of the moon as seen from Earth first, and then will attempt the rest. I have thus far, ω=\int\intsin θ dθ dφ, where the first integral goes from 0 to 2pi and the second from 0 to θ, but I'm lost as to how to solve it.

Anthony

 

[malawi_glenn]

Aren't you forgetting the distance ?

http://www.schorsch.com/kbase/glossary/solid_angle.html