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Question
In the given figure, if tan θ = `(5)/(13), tan α = (3)/(5)` and RS = 12m, find the value of 'h'.
Solution
tan θ = `"PQ"/"QS"`
⇒ `(5)/(13) = "h"/"QS"`
⇒ 5 x QS = 13h
⇒ 5(QR + RS) = 13h
⇒ 5(QR + 12) = 13h
⇒ QR + 12 = `(13"h")/(5)` ....(i)
tan α = `"PQ"/"QR"`
⇒ `(3)/(5) = "h"/"QR"`
⇒ 3 x QR = 5h
⇒ QR = `(5"h")/(3)` ....(ii)
Substituting (ii) in (i), we have
`(5"h")/(3) + 12 = (13"h")/(3)`
⇒ `(13"h")/(5) - (5"h")/(3)` = 12
⇒ `(39"h" - 25"h")/(15)` = 12
⇒ 14h = 180
⇒ h = 12.86m.
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