for positive acute angles A and B, it is known that tan A = 11/60 and sin B = 28/53. Find the value of sin (A + B) in simplest form.

Question

I would appreciate if you could show steps as I am confused.

Answer 1

tanA = 11/60; cosA = 1/√1 + (11/60)² = 60/61; sinA = tanAcosA = 11/60·60/61 = 11/61;

cosB = √1 - (28/53)² = 45/53;

sin(A + B) = sinAcosB + cosAsinB = (11/61)(45/53) + (60/61)(28/53) = 2175/3233