Theory question 102
TrigonometryIf sin A = 3/5 and cos B = 15/17, where A is obtuse and B is acute, find the value of cos(A + B).
Show the model answer
Model answer
A is obtuse, so cos A = −4/5
B is acute, so sin B = 8/17
cos(A + B) = cos A cos B − sin A sin B
= (−4/5)(15/17) − (3/5)(8/17) = −60/85 − 24/85
= −84/85
Explanation
Use right-angled triangles (3, 4, 5 and 8, 15, 17) and remember cosine is negative for an obtuse angle.