SOLUTION: D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is m DEF?

Algebra ->  Triangles -> SOLUTION: D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is m DEF?      Log On


   

Question 865636: D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is
m DEF?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
DE, sqrt%28%284-5%29%5E2%2B%283-7%29%5E2%29=sqrt%281%2B9%29=highlight%28sqrt%2810%29%29

EF, sqrt%28%288-4%29%5E2%2B%282-3%29%5E2%29=sqrt%2816%2B1%29=highlight%28sqrt%2817%29%29

FD, sqrt%28%285-8%29%5E2%2B%287-2%29%5E2%29=sqrt%289%2B25%29=highlight%28sqrt%2834%29%29


Use Law Of Cosines.
Using c for measure of angle DEF,
highlight_green%28FD%5E2=DE%5E2%2BEF%5E2-2%2ADE%2AEF%2Acos%28c%29%29.
-2%2ADE%2AEF%2Acos%28c%29=FD%5E2-DE%5E2-EF%5E2
cos%28c%29=%28DE%5E2%2BEF%5E2-FD%5E2%29%2F%282%2ADE%2AEF%29
Substitute the found values.
cos%28c%29=%2810%2B17-34%29%2F%282%2Asqrt%2810%2A17%29%29
cos%28c%29=-7%2F%282%2Asqrt%28170%29%29
highlight_green%28cos%28c%29=-0.2684%29.
c = 105.6 degrees