Answer:
-16/65
Explanation:
We can use the sum formula for sine to find sin(a+b):
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
We are given the values of sin(a) and sin(b), but we don't have the values of cos(a) and cos(b). However, we can use the Pythagorean identity to find them:
sin^2(a) + cos^2(a) = 1 => cos^2(a) = 1 - sin^2(a)
sin^2(b) + cos^2(b) = 1 => cos^2(b) = 1 - sin^2(b)
We know that angle A is acute, so cos(a) is positive. For angle B, we know that it is obtuse, which means that cos(b) is negative. With this information, we can find the values of cos(a) and cos(b):
cos(a) = sqrt(1 - sin^2(a)) = sqrt(1 - (3/5)^2) = 4/5
cos(b) = -sqrt(1 - sin^2(b)) = -sqrt(1 - (5/13)^2) = -12/13
Now we can substitute these values into the sum formula for sine:
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
= (3/5)(-12/13) + (4/5)(5/13)
= -36/65 + 20/65
= [-16/65]