Question

Find AB.

Answer 1

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.