You can pretty much calculate any angle using trigonometric functions. These functions work with right triangles but will provide answers for any triangle that can be broken into two right triangles.
Given the illustration:
The sine of the angle a is a ratio of the length of the opposite side to the length of the hypotenuse.
The cosine of the angle a is a ratio of the length of the adjacent side to the length of the hypotenuse.
The tangent of the angle a is a ratio of the length opposite side to the length of the adjacent side.
Just in case you do not know ratio means divided by.
Knowing the length of any two sides of the triangle we can calculate either the sine, cosine or tangent and from that determine the angle.
Since the sum of the three angles of a triangle must be 180o
and one angle of a right triangle is always 90o
we can calculate the third angle.
As an example suppose the adjacent side is 6 inches and the hypotenuse is 8 inches, we can calculate the cosine of angle a as 6/8 = .750 . If we check the trig tables or a fancy calculator we see that .750 is the cosine of the angle 41.41o
. If you don't have a fancy calculator and you are using the tables you might have to interpolate. (But thats another story).
Given that the unknown angle = 180-(90+41.41) the three angles are 41.41, 90 and 48.59.
There are other trignometric functions, but sine, cosine and tangent will do the bulk of the work.