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Question Number 212214 by CrispyXYZ last updated on 06/Oct/24

Find tanθ.

Findtanθ.

Commented by CrispyXYZ last updated on 06/Oct/24

Answered by a.lgnaoui last updated on 06/Oct/24

sin 𝛉=((CD)/(BC))      BC=2(√2)    CD=2(√2) sin 𝛉   AD^2 =1+CD^2 −2CDcos (180−𝛉)   9=1+8sin^2 𝛉+2(√2) sin 2𝛉  8=8sin^2 𝛉+2(√2) sin 2𝛉     sin 2𝛉=2(√2) (1−sin^2 𝛉)  sin 𝛉(√(1−sin^2 𝛉))=(√2) (1−sin^2 𝛉)  sin 𝛉=(√(2(1−sin^2 𝛉)))     3sin^2 𝛉−2=0 ⇒  sin 𝛉=(√(2/3))  ;(𝛉<90)                    𝛉=54,735

sinθ=CDBCBC=22CD=22sinθAD2=1+CD22CDcos(180θ)9=1+8sin2θ+22sin2θ8=8sin2θ+22sin2θsin2θ=22(1sin2θ)sinθ1sin2θ=2(1sin2θ)sinθ=2(1sin2θ)3sin2θ2=0sinθ=23;(θ<90)θ=54,735

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