Question

The moon's distance from the earth is 360000km and its diameter subtends an angle of 42' at the eye of the observer.The diameter of the moon is?

Answer 1

I calculate ~ 4398 km

Explanation:

The diameter of the moon is 2 times the radius of the moon, which I'll call `r` (little r).

If the diameter subtends an angle of 42', then the radius subtends an angle of half this value, or 21'.

...this is `21/60 = 0.35` degrees.

...make sure your calculator is set for degrees, not radians...

`r/360000 = sin(0.35 degrees) = 0.00611`

`r = 2199 km`

Which would make the diameter be `2199 * 2 = 4398` km

...incidentally, a google search returns a value of 3474 km for the moon's diameter.

Based on the numbers given in the problem statement, though, 4398 is what we calculate.