What is the exact value of the following trig problem...?

Question

Sin A = 5/13

Sin B = 6/ sqtr 85

Cos A = 5/12

Cos B = 6/7

What is the exact value of Sin(A+B)?


So far I have got 30/91 + 30/12rt85 and am unsure if this is correct.

Answer 1

sin(a+b) = sin a cos b + sin b cos a
sin(a+b) = 5/13 • 6/7 + 6/√85 • 5/12
sin(a+b) = 30/91 + 5/ 2√85

this is what you have, but I simplified the 2nd fraction a bit. the next thing to do is add the fractions after rationalizing the denominator of the 2nd.

sin(a+b) = 30/91 + (5√85)/170
sin(a+b) = 30/91 + (√85)/24
sin(a+b) = (720 + 91√85)/2184

Answer 2

It is 0.8927522....

Since they want an exact answer this won't work. You're answer comes out to about 0.6008 (feel free to check that math). Using a scientific calculator I took the inverse sin's of 6/sqrt 85 and 5/13. Then I took those two answers, added them together, and took the sin of that. I forget how to get the *exact* number using only paper, so just compare any answer you get with 0.8927522.... and if it is very close, you should be good.

Edit*** It looks like they used different values for A&B between cos and sin. I don't believe my answer works here.

Answer 3

Sin(A+B)= Sin A.Cos B +Sin B.Cos A
= 5/13 * 5/12 + 6/sqrt 85 * 6/7
=25/156 +36 /(7* sqrt 85)
Thats it! Nothing more nothing less!