Question

In a triangle, the sides measure 3,5, and 7 what is the measure, in degrees of the largest angle?

Answer 1

`The\ largest\ angle\ is\ opposite\ the\ largest\ side.\\look\ at\ the\ picture.\\\\Law\ of\ cosines:\\\\c^2=a^2+b^2-2abcos\alpha\\\\a=3;\ b=5;\ c=7\\\\substitute:`


`7^2=3^2+5^2-2\cdot3\cdot5\cdot cos\alpha\\49=9+25-30cos\alpha\\49=34-30cos\alpha\\30cos\alpha=34-49\\30cos\alpha=-15\ \ \ \ /:30\\cos\alpha=-(15)/(30)\\\\cos\alpha=-(1)/(2)\\\\\alpha=120^o`