How do I find the angles of a right triangle with only the sides

If you want to know the size of angle A and you know the value of the side opposite ∠A (side a) and you know the value of the hypotenuse (side c), use sine:  

     sin(A) =  opposite / hypotenuse   --->   sin(A) = a/c   --->   A  =  sin^-1(a/c)

If you want to know the size of angle A and you know the value of the side adjacent ∠A (side b) and you know the value of the hypotenuse (side c), use cosine:  

     cos(A) =  adjacent/ hypotenuse   --->   cos(A) = b/c   --->   A  =  cos^-1(b/c)

If you want to know the size of angle A and you know the value of the side opposite ∠A (side a) and you know the value of the side adjacent ∠A (side b), use tangent:  

     tan(A) =  opposite / adjacent   --->   tan(A) = a/b   --->   A  =  tan^-1(a/b)