Question #7812

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

Expert's answer

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

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

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