SOLUTION: the two legs of a triangle are 300 and 150 m each, respectively. The angle opposite the 150 m side is 26 degree. What is the 3rd side?

Algebra ->  Trigonometry-basics -> SOLUTION: the two legs of a triangle are 300 and 150 m each, respectively. The angle opposite the 150 m side is 26 degree. What is the 3rd side?      Log On


   

Question 770249: the two legs of a triangle are 300 and 150 m each, respectively. The angle opposite the 150 m side is 26 degree. What is the 3rd side?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Draw what you describe. If your unknown side length is the number, c, then you can form an equation using Law of Cosines:

highlight%28300%5E2%2Bc%5E2-2%2Ac%2A300%2Acos%2826%29=150%5E2%29
c%5E2-600%2Acos%2826%29c%2B300%5E2-150%5E2=0 Quadratic Equation with Variable, c.
c%5E2-539.28c%2B67500=0
c=%28539.28%2Bsqrt%28539.28%5E2-4%2A67500%29%29%2F2
c=%28539.28%2Bsqrt%2820819.066%29%29%2F2
c=341.784,
better to say based on provided accuracy
highlight%28c=342%29