Question 865636
DE, {{{sqrt((4-5)^2+(3-7)^2)=sqrt(1+9)=highlight(sqrt(10))}}}


EF, {{{sqrt((8-4)^2+(2-3)^2)=sqrt(16+1)=highlight(sqrt(17))}}}


FD, {{{sqrt((5-8)^2+(7-2)^2)=sqrt(9+25)=highlight(sqrt(34))}}}



Use Law Of Cosines.
Using c for measure of angle DEF,
{{{highlight_green(FD^2=DE^2+EF^2-2*DE*EF*cos(c))}}}.
{{{-2*DE*EF*cos(c)=FD^2-DE^2-EF^2}}}
{{{cos(c)=(DE^2+EF^2-FD^2)/(2*DE*EF)}}}
Substitute the found values.
{{{cos(c)=(10+17-34)/(2*sqrt(10*17))}}}
{{{cos(c)=-7/(2*sqrt(170))}}}
{{{highlight_green(cos(c)=-0.2684)}}}.
c = 105.6 degrees