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 60° = `"AB"/"BC"`

`sqrt(3) = "AB"/x`
 x = `"AB"/sqrt(3)`         ...(2)
From (1)

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

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

2AB = `20sqrt(3)`

2AB = `(20sqrt(3))/(2)`

AB = `10sqrt(3)`

AB = 17.32 cm

From (2)

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

x = `(17.32)/sqrt(3)`

x = 10 cm

Therefore BC = x = 10 cm
Therefore, AB = 17.32 cm, BC = 10 cm.