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Question
Find x and y, in each of the following figure:
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Solution
In right ΔABC,
tan30° = `"BC"/"AB"`
⇒ `(1)/sqrt(3) = x/(24 + y)` ....(i)
In right ΔDBC,
tan60° = `"BC"/"DB"`
⇒ `sqrt(3) = x/y`
⇒ x = `sqrt(3)y`
Substituting the value of x in (i), we get
`(1)/sqrt(3) = sqrt(3)/(24 + y)`
⇒ 24 + y = 3y
⇒ 2y = 24
⇒ y = 12cm
⇒ x = `sqrt(3) xx 12 = 12sqrt(3)"cm"`.
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