Question

If tan x° = `(5)/(12)`,

tan y° = `(3)/(4)` and AB = 48 m; find the length of CD.

Answer 1

Given tan x° = `(5)/(12)` tan t° = `(3)/(4)` and AB = 48 m;

Let length of  BC = x m

From ΔADC

tan x°  = `"DC"/"AC"`

`(5)/(12) = "DC"/(48 + x)`

240 + 5x = 12 CD     ...(1)

Also, from ΔBDC

tan y° = `"CD"/"BC"`

`(3)/(4) = "CD"/x`

x = `(4"CD")/(3)`       ...(2)

From (1)

240 + 5 `((4"CD")/(3))` = 12CD

240 + `(20"CD")/(3)` = 12CD

720 + 20CD = 36CD

16CD = 720

CD = 45

Therefore, length of CD is 45 m.