SOLUTION: If the sides a triangle have measurements of 7,8, & 10, how do I find the angles within the triangle? Thank you.

Algebra ->  Triangles -> SOLUTION: If the sides a triangle have measurements of 7,8, & 10, how do I find the angles within the triangle? Thank you.      Log On


   

Question 520544: If the sides a triangle have measurements of 7,8, & 10, how do I find the angles within the triangle?
Thank you.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Sides are 7,8, & 10
That's the side-side-side case.  It's done by the law of cosines.





cos%28A%29 = %28b%5E2%2Bc%5E2-a%5E2%29%2F%282bc%29 = %288%5E2%2B7%5E2-10%5E2%29%2F%282%2A8%2A7%29
cos%28B%29 = %28a%5E2%2Bc%5E2-b%5E2%29%2F%282ac%29 = %2810%5E2%2B7%5E2-8%5E2%29%2F%282%2A10%2A7%29
cos%28C%29 = %28a%5E2%2Bb%5E2-c%5E2%29%2F%282ab%29 = %2810%5E2%2B8%5E2-7%5E2%29%2F%282%2A10%2A8%29

If you calculate those, and take inverse cosines, you'll get

A = 83.33457274°,  B = 52.61680158°,  C = 44.04862567°

Edwin