Answer to Question #7812 in Trigonometry for Amanda Radke

Question

In parallelogram EFGH, EH=8, EF=11, and the measure of angle E is 110 degrees. Find the measure of diagonals HF amd EG

Answer 1

Since it parallelogram,
FG+EH
EF=GH
& angle F=180-angle E=180-110=70
Then we can use cosine rule to find diagolnals:
1. consider triangle EFG
EG^2=EF^2+FG^2-2*EF*FG*cosF=11^2+8^2-2*8*11*cos(70)=12,4^2
2. consider triangle EFH

FH^2=EF^2+EH^2-2*EF*EH*cosE=11^2+8^2-2*8*11*cos(110)=15,7^2
So the diagonals are 12,4 and 15,7