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Question
If tan x° = `(5)/(12)`,
tan y° = `(3)/(4)` and AB = 48 m; find the length of CD.
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Solution
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.
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