If sin(26)+sin(24)=Sin(A), 0<A<90, then A=____ degrees.

Question

I know this is with the sum-to-product identity, but I need help with the steps.

Answer 1

sin(26)+sin(24)=sin(A)

sin(a)+sin(b)=2sin[(a+b)/2]cos[(a-b)/2]

a=26, b=24

2sin(26+24)/2*cos(26-24)/2

2sin(25)*cos(1)

2(0.42261)(0.99984)

0.845084=sin(A)

arcsin(0.845084)=57.6809369º or 57º 40' 51.373"

 

Answer 2

sin26° + sin24° = sinA

 

A = sin^-1(sin26° + sin24°) ≅ 57.68°