α and β are acute angles in quadrant I, with sin α = 7/25 and cos B = 5/13. Determine the value of sin (α + β)

The answer is 323 / 325

I started with
sin (α + β) = sin α cos β + cos α sin β
α = 7/25
B = 5/13
sin (7/25) cos (5/13) + cos (7/25) sin (5/13)

Is that even right? If so, where do you go from there?

2. I started with
sin (α + β) = sin α cos β + cos α sin β
α = 7/25 no
B = 5/13 no
sin (7/25) cos (5/13) + cos (7/25) sin (5/13) and no
you were given values for sin a and cos b ... sketch reference triangles in quad I for each angle, then determine cos a and sin b

sin a = 7/25 ... cos a = 24/25

cos b = 5/13 ... sin b = 12/13

sin(a+b) = sin a cos b + cos a sin b

sin(a+b) = (7/25)(5/13) + (24/25)(12/13)

3. Oh, ok. I get it now. Thanks

4. Originally Posted by lanvin
α and β are acute angles in quadrant I, with sin α = 7/25 and cos B = 5/13. Determine the value of sin (α + β)

The answer is 323 / 325

I started with
sin (α + β) = sin α cos β + cos α sin β
α = 7/25
B = 5/13
sin (7/25) cos (5/13) + cos (7/25) sin (5/13)

Is that even right? If so, where do you go from there?
You're on the right track. Another way is to remember

$\displaystyle \cos^2{x} + \sin^2{x} = 1$.

You can use this to find $\displaystyle \cos{\alpha}$ and $\displaystyle \sin{\beta}$.