Answer:
EH = 52
Step-by-step explanation:
Using right triangle FGH
Applying Pythagoras' identity
FH² + HG² = FG²
FH² + 80² = 89²
FH² + 6400 = 7921 ( subtract 6400 from both sides )
FH² = 1521 ( take square root of both sides )
FH = [tex]\sqrt{1521}[/tex] = 39
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Using right triangle EFH
Applying Pythagoras' identity
FH² + EH² = EF²
39² + EH² = 65²
1521 + EH² = 4225 ( subtract 1521 from both sides )
EH² = 2704 ( take square root of both sides )
EH = [tex]\sqrt{2704}[/tex] = 52
