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 882689: D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is
m DEF?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Calculate the edge lengths,
DE%5E2=%285-4%29%5E2%2B%287-3%29%5E2
DE%5E2=1%2B16
DE%5E2=17
.
.
DF%5E2=%285-8%29%5E2%2B%287-2%29%5E2
DF%5E2=9%2B25
DF%5E2=34
.
.
EF%5E2=%284-8%29%5E2%2B%283-2%29%5E2
EF%5E2=16%2B1
EF%5E2=17
.
.
The triangle is an isosceles (two equal sides) and right triangle (DE%5E2%2BEF%5E2=DF%5E2).
So then the angles are 45-45-90.
Angle DEF is 90.