Question

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

Answer 1

In right ΔABC,

tan45° = `"AB"/"BC"`

⇒ 1 = `x/(15 + y)`
⇒ x = 15 + y       ....(i)
In right ΔABD,

tan60° = `"AB"/"BD"`

⇒ `sqrt(3) = x/y`

⇒ `sqrt(3) = (15 + y)/y`   ....[From (i)]

⇒ `sqrt(3)y` = 15 + y
⇒ `sqrt(3)y - y` = 15
⇒ `y(sqrt(3) - 1)` = 15

⇒ y = `(15)/(sqrt(3) - 1)`

⇒ y = `(15)/(sqrt(3) - 1) xx (sqrt(3) + 1)/(sqrt(3) + 1`

= `(15(sqrt(3) + 1))/(3 - 1)`

= `(15(sqrt(3) + 1))/(2)"cm"`

⇒ x = `15 + (15(sqrt(3) + 1))/(2)`

= `(30 + 15(sqrt(3) + 1))/(2)`

= `(15(2 + sqrt(3) + 1))/(2)`

= `(15(3 + sqrt(3)))/(2)`

= `(15sqrt(3)(sqrt(3) + 1))/(2)`.