SOLUTION: Given that A and B are acute angles such that sin A = 3/5 and cos B = 5/13, calculate the value of sin(A+B)

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Question 1092330: Given that A and B are acute angles such that sin A = 3/5 and cos B = 5/13, calculate the value of sin(A+B)
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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1.  Since sin(A) = 3%2F5,  cos(A) = sqrt%281+-+sin%5E2%28A%29%29 = sqrt%281-%283%2F5%29%5E2%29 = sqrt%281-9%2F25%29 = sqrt%2825-9%29%2F25%29 = sqrt%2816%2F25%29 = 4%2F5%29.


2.  Since cos(B) = 5%2F13,  sin(B) = sqrt%281+-+cos%5E2%28B%29%29 = sqrt%281-%285%2F13%29%5E2%29 = sqrt%281-25%2F169%29 = sqrt%28169-25%29%2F169%29 = sqrt%28144%2F169%29 = 12%2F13%29.


3.  Now sin(A+B) = sin(A)*cos(B) + cos(A)*sin(B) = %283%2F5%29%2A%285%2F13%29+%2B+%284%2F5%29%2A%2812%2F13%29 = 15%2F65+%2B+48%2F65 = 63%2F65.

Answer.  sin(A+B) = 63%2F65.