I need help with trig ASAP !

Question

We know the following values.

sinA=4/5

cosB=√3/2

Give the exact value of Sin(A+B)

Answer 1

I'm guessing you're using the sum identities

sin(A+B) = sin(A)cos(B) + sin(B)cos(A)

We're given sin(A) and cos(B)

Now we just need cos(A) and sin(B)

To get cos A, we can construct a triangle.

sin(A) = 4/5, so make a triangle with angle A and 4 being the opposite side and 5 being the hypotenuse.

We get a 3-4-5 triangle here and see that cos(A) = 3/5

We also could have used the property: sin²A + cos²A = 1 and solved.

(4/5)² + cos²A = 1

cos²A = 1 - (4/5)² = 9/25

cos A = √(9/25) = 3/5

Solve for sin(B) in a similar way and plug into the first equation