Question

Find AB and BC, if:

Answer 1

Let  BC = x m

BD = BC + CD = (x + 20) cm

In ΔABD,
tan 45° = `"AB"/"BD"`

1 = `"AB"/(x + 20)`

x + 20 = AB      ...(1)

In ΔABC

tan 60° = `"AB"/"BC"`

`sqrt(3) = "AB"/x`

x = `"AB"/sqrt(3)`      ...(2)

From (1)

`"AB"/sqrt(3) + 20 = "AB"`

AB + `20sqrt(3) = sqrt(3)"AB"`

AB`(sqrt(3) -1) = 20sqrt(3)`

AB = `(20sqrt(3))/((sqrt(3) - 1)`

AB = `(20sqrt(3))/((sqrt(3) - 1)) xx ((sqrt(3)+1))/((sqrt(3)+1)`

AB = `(20sqrt(3)(sqrt(3) + 1))/(3 - 1)`

AB = 47.32 cm

From (2)

x = `"AB"/sqrt(3)`

x = `(47.32)/sqrt(3)`

x = 27.32 cm

∴ BC = x = 27.32 cm

Therefore, AB = 47.32 cm, BC = 27.32 cm.