SOLUTION: The Laws of Sines and Cosines solve triangle ABC a=8, measure of angle A=60 degrees, measure of angle c=40 degrees

Algebra ->  Trigonometry-basics -> SOLUTION: The Laws of Sines and Cosines solve triangle ABC a=8, measure of angle A=60 degrees, measure of angle c=40 degrees       Log On


   

Question 717501: The Laws of Sines and Cosines
solve triangle ABC
a=8, measure of angle A=60 degrees, measure of angle c=40 degrees
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First the east part. Since we know two of the angles and since the 3 angles must add up to 180, angle B = 180 - (60 + 40) = 180 - 100 = 80.

We can use the Law of Sins to find the missing sides. First side b:
sin%28B%29%2Fb+=+sin%28A%29%2Fa
Substituting what we know:
sin%28100%29%2Fb+=+sin%2860%29%2F8
Cross-multiplying:
8%2Asin%28100%29+=+b%2Asin%2860%29
Dividing by sin(60):
%288%2Asin%28100%29%29%2Fsin%2860%29+=+b
I'll leave it up to you and your calculator to finish this.

For side c:
sin%28C%29%2Fc+=+sin%28A%29%2Fa
Substituting what we know:
sin%2840%29%2Fc+=+sin%2860%29%2F8
Cross-multiplying:
8%2Asin%2840%29+=+c%2Asin%2860%29
Dividing by sin(60):
%288%2Asin%2840%29%29%2Fsin%2860%29+=+c
Again, I'll leave it up to you and your calculator to finish this.