SOLUTION: Use the Law of Sines to solve the triangle. (Round your answers to two decimal places. If there is no solution, enter NO SOLUTION.) β = 76°, b = 13, c = 6 I got a=13.07 but

Algebra ->  Trigonometry-basics -> SOLUTION: Use the Law of Sines to solve the triangle. (Round your answers to two decimal places. If there is no solution, enter NO SOLUTION.) β = 76°, b = 13, c = 6 I got a=13.07 but       Log On


   

Question 728368: Use the Law of Sines to solve the triangle. (Round your answers to two decimal places. If there is no solution, enter NO SOLUTION.)
β = 76°, b = 13, c = 6
I got a=13.07 but every time I try and plug the information in the law of sines it says i get it wrong?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28beta%29%2Fb=sin%28gamma%29%2Fc
sin%28gamma%29=c%2Asin%28beta%29%2Fb
Plugin the values:
sin%28gamma%29=6%2Asin%2876%29%2F13
sin%28gamma%29=0.4478
highlight%28gamma+=+26.6%29 degrees.

You have two angles of the triangle and you can use sum to 180 degrees to find the measure of angle alpha.

76%2B26.6%2Balpha=180
highlight%28alpha=77.4%29 degrees.

Use Law of Sines again to find the length of a.
sin%28alpha%29%2Fa=sin%28beta%29%2Fb
a%2Fsin%28alpha%29=b%2Fsin%28beta%29
a=b%2Asin%28alpha%29%2Fsin%28beta%29
a=13%2Asin%2877.4%29%2Fsin%2876%29
a=... What do you get? This should be very very near 13.