First find the side lengths of the box by factoring each area:
12: 1, 2, 3, 4, 6, 12
15: 1, 3, 5, 15
20: 1, 2, 4, 5, 10, 20
Find 3 numbers that both have 2 sides have in common and can multiply to make the areas of the faces:
12: 3 * 4
15: 3 * 5
20: 4 * 5
Sides: 3, 4, and 5
Then multiply to get the volume:
3 * 4 * 5 = 60 units^2
We have the formula (sin x)^2 + (cos x)^2 = 1;
Then, sin α =

cos β =

We apply the formula sin ( α + β ) = sin α x cos β + sin β x cos α = (3/5)x(4/5) + (4/5)x(3/5) = 12/25 + 12/25 = 24/25;
That would be A, 22/12 and 27/12