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If tan Θ = 1 2 then what is sin Θ?

User Gmoshkin
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tanx=12 is the same as saying that tanx=12/1. We know that tanx is opposite over adjacent. If you draw out a triangle with x in an angle and 12 on the opposite length and 1 on the adjacent, pythagorean theorem can be used to find the hypotenuse, since sinx is opposite over hypotenuse. The hypotenuse is the square root of 145, and therefore sinx is 12/√145
User Beau Trepp
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1 vote

Answer : The value of
\sin \theta is,
(1)/(√(5))

Step-by-step explanation :

Given:


\tan \theta=(1)/(2)

According to trigonometric function,


\tan \theta=(Perpendicular)/(Base)=(1)/(2)

To make a ΔABC:

Thus,

Side AB = 1x

Side BC = 2x

Now we have to determine the side AC.

Using Pythagoras theorem in ΔABC :


(Hypotenuse)^2=(Perpendicular)^2+(Base)^2


(AC)^2=(AB)^2+(BC)^2

Now put all the values in the above expression, we get the value of side AC.


(AC)^2=(1x)^2+(2x)^2


AC=√((1x)^2+(2x)^2)


AC=√(5)x

Now we have to determine the value of
\sin \theta

According to trigonometric function,


\sin \theta=(Perpendicular)/(Hypotenuse)=(1x)/(√(5)x)


\sin \theta=(1)/(√(5))

Thus, the value of
\sin \theta is,
(1)/(√(5))

If tan Θ = 1 2 then what is sin Θ?-example-1
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