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Question
Find AB and BC, if:
Solution
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.
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