In parallelogram EFGH, EH=8, EF=11, and the measure of angle E is 110 degrees. Find the measure of diagonals HF amd EG
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Expert's answer
2012-03-27T08:18:27-0400
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
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