Advertisements
Advertisements
Question
In the given figure, if tan θ = `(5)/(13), tan α = (3)/(5)` and RS = 12m, find the value of 'h'.
Advertisements
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.
APPEARS IN
RELATED QUESTIONS
If 2 sin x° − 1 = 0 and x° is an acute angle; find:
- sin x°
- x°
- cos x° and tan x°.
If 3 tan A - 5 cos B = `sqrt3` and B = 90°, find the value of A
Find the value of 'A', if `sqrt(3)cot"A"` = 1
If θ = 30°, verify that: tan2θ = `(2tanθ)/(1 - tan^2θ)`
If A = B = 60°, verify that: sin(A - B) = sinA cosB - cosA sinB
Find the value of: `sqrt((1 - sin^2 60°)/(1 + sin^2 60°)` If 3 tan2θ - 1 = 0, find the value
a. cosθ
b. sinθ
Find the value 'x', if:
If tan x° = `(5)/(12) . tan y° = (3)/(4)` and AB = 48m; find the length CD.
Evaluate the following: cosec 54° - sec 36°
Evaluate the following: `(5sec68°)/("cosec"22°) + (3sin52° sec38°)/(cot51° cot39°)`
