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Home >> Trigonometry Ratios >> Examples

## Find ratio of Sin, Cosec, Cos, Sec, Tan and Cot - Trigonometry : Solved Examples

 T Ratios of Angles - 30, 45, 60 & 90 degree angles Find Height, Distance using T - Ratios

If cos Theta = 2/3, find sin and tan theta
Lets draw the right angle triangle with the above mentioned details

Given thing are
cos Θ = 2/3

we know that Cos Θ = Adjacent Side / Hypotenuse, so we get

Hypotenuse = 3

Hypotenuse : BC = 3
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

 __ AC = √ 5

So Sin, Cos and Tan will be as follows -

Sin Θ = Opposite Side / Hypotenuse
 __ Sin Θ = √ 5  / 3

Tan Θ = Opposite Side / Adjacent Side
 __ Tan Θ = √ 5  / 2

Cos Θ = Adjacent Side / Hypotenuse
Cos Θ = 2/3

### Related Question Examples

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