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Question
Find AB.
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Solution
Consider the figure
From right triangle ACF
tan 45° = `(20)/"AC"`
1 = `(20)/"AC"`
AC = 20 cm
From triangle DEB
tan 60° = `(30)/"BD"`
`sqrt(3) = (30)/"BD"`
BD = `(30)/sqrt(3)` = 17.32 cm
Given FC = 20, ED = 30, So EP = 10 cm
Therefore
tan 60° = `"FP"/"EP"`
`sqrt(3)= "FP"/(10)`
FP = `10sqrt(3)` = 17.32 cm
Thus AB = AC + CD + BD = 54.64 cm.
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