Given thing are
cos Θ = 2/3
we know that Cos Θ = Adjacent Side / Hypotenuse, so we get
Adjacent Side = 2
Hypotenuse = 3
Hypotenuse : BC = 3
Adjacent Side : AB = 2 (Adjacent to ∠ Θ)
Opposite Side : AC = ? (Opposite to ∠ Θ)
To find the Opposite Side - AC , we use Pythagoras theorem ((Hypotenuse)2 = (Leg 1)² + (Leg 2)²)
AC = √ BC² - AB²
AC = √ 32 - 22
AC = √ 9 - 4
AC = √5
Now we will try to simplify square root of 5. As no pairs can be made the final value will be
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AC = √ 5
So Sin, Cos and Tan will be as follows -
Sin Θ = Opposite Side / Hypotenuse
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Sin Θ = √5/3
Tan Θ = Opposite Side / Adjacent Side
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Tan Θ = √5/2
Cos Θ = Adjacent Side / Hypotenuse
Cos Θ = 2/3