SOLUTION: Find the largest angle of the Triangle whose sides are 7cm,5cm,3cm

Algebra ->  Triangles -> SOLUTION: Find the largest angle of the Triangle whose sides are 7cm,5cm,3cm      Log On


   

Question 1028875: Find the largest angle of the Triangle whose sides are 7cm,5cm,3cm
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the largest angle of the Triangle whose sides are 7cm,5cm,3cm
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

The largest angle  alpha  is opposite to the longest side, which is 7 cm.

So from the Cosines Law theorem  (see, for example, the lesson  Proof of the Law of Cosines revisited  in this site),  you have 


7%5E2 = 5%5E2+%2B+3%5E2+-+2%2A5%2A3%2Acos%28alpha%29,   or

49 = 25+%2B+9+-+30%2Acos%28alpha%29,   or

49+-+25+-+9 = -30%2Acos%28alpha%29,   or

15 = -30%2Acos%28alpha%29,   or

cos%28alpha%29 = -15%2F30 = -1%2F2.

Hence,  alpha = 120 degrees.

Answer.  alpha = 120 degrees.