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If sin a=3/5 and sin b= 5/13, where A is an acute angle, B is an obtuse angle. find sin (a+b)​

User Aep
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1 Answer

1 vote

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]

User Hgcummings
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