Question

if a and b are the measures of two first quadrant angles and sin a = 4/5 and sin b = 5/13, find sin a+b

Answer 1

angle addition property
\[\sin(a+b) = \sin a \cos b + \sin b \cos a\]

Answer 2

also
\[\sin^{2} \theta + \cos^{2} \theta = 1\]
this is how you can find cos(a) and cos(b)

Answer 3

I tried to to that but got (20/39)+(1/3) or 11/13. The available answers are
(63/65)
(33/65)
(16/65)
(56/65)

Answer 4

@dumbcow

Answer 5

looks like you didn't get the right values for cos(a) and cos(b)

cos a = 3/5

cos b = 12/13

Answer 6

So it would be sin(a+b)=(4/5)(12/13)+(3/5)(5/13) = 63/65?

Answer 7

correct

Answer 8

Thanks!

Answer 9

try to go back and see what you did wrong in finding the cosine values