Question

Find x and y, in each of the following figure:

Answer 1

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"`.