Question 921229
let A = u and B = v


you have:


sine of A = 5/13
cosine of B = -3/5


both angles are in the second quadrant.


use the pythagorean formula to solve for the missing leg of each triangle.


you will get:


side opposite A = 5
side adjacent A = -12
hypotenuse A = 13


side opposite B = 4
side adjacent B = -3
hypotenuse B = 5


the side adjacent is negative in both triangles because they are both in the second quadrant where the value of x is negative while the value of y is positive.


now that you know the sides, you can solve for tangent of A and tangent of B.


tangent of A will be equal to 5 / -12 which is equal to -5/12.


tangent of B will be equal to 4 / -3 which is equal to -4/3.


tangent of A+B is equal to (tangent of A plus tangent of B) divided by (1 - tangent of A * tangent of B).


plug values in for the words and you get:


tangent of A plus B = ((-5/12) - (4/3)) divided by (1 - (-5/12 * -4/3)


do the arithmetic and this turns out to be:


tangent of A plus B = -1.75 / .4444444 which is equal to -3.9375.


that's your solution.


you can translate this back to u and v by letting u = A and v = B and you get:


tan(u+v) = -3.9375.