Question

Find AB and BC, if:

Answer 1

Let BC = x m

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

In ΔABD,

tan 30° = `"AB"/"BD"`

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

x + 20 = `sqrt(3)"AB"`           .....(1)

In ΔABC

tan 45° = `"AB"/"BC"`

1 = `"AB"/x`

AB = x         ...(2)

From (1)

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

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

AB = `(20)/((sqrt3 - 1))`

= `(20)/((sqrt3 - 1)) xx ((sqrt(3) + 1))/((sqrt(3) + 1))`

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

= 27.32cm

From (2)

AB = x = 27.32 cm

Therefore BC = x = AB = 27.32 cm

Therefore, AB = 27.32 cm, BC = 27.32 cm