SOLUTION: The sides of a triangle are 3 cm, 5 cm and 7 cm respectively. Show that the largest angle is 120 degree, and find the area of the triangle.

Algebra ->  Triangles -> SOLUTION: The sides of a triangle are 3 cm, 5 cm and 7 cm respectively. Show that the largest angle is 120 degree, and find the area of the triangle.       Log On


   

Question 1076294: The sides of a triangle are 3 cm, 5 cm and 7 cm respectively. Show that the largest angle is 120 degree, and find the area of the triangle.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Using the law of cosines,
c%5E2=a%5E2%2Bb%5E2-2ab%2Acos%28C%29
cos%28C%29=%28a%5E2%2Bb%5E2-c%5E2%29%2F%282ab%29%29
So,
cos%28C%29=%283%5E2%2B5%5E2-7%5E2%29%2F%282%283%29%285%29%29
cos%28C%29=%289%2B25-49%29%2F30
cos%28C%29=%28-15%29%2F30
cos%28C%29=-1%2F2
C=120
.
.
.
To find the area, use Heron's formula,
S=%283%2B5%2B7%29%2F2=15%2F2
So then,
A=sqrt%28S%28S-3%29%28S-5%29%28S-7%29%29
A=sqrt%28%2815%2F2%29%2815%2F2-6%2F2%29%2815%2F2-10%2F2%29%2815%2F2-14%2F2%29%29
A=sqrt%28675%2F16%29
A=%2815%2F4%29sqrt%283%29