Question

If tan Θ = 1 2 then what is sin Θ?

Answer 1

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

Answer 2

Answer : The value of $\sin \theta$ is, $\frac{1}{\sqrt{5}}$

Step-by-step explanation :

Given:

$\tan \theta=\frac{1}{2}$

According to trigonometric function,

$\tan \theta=\frac{Perpendicular}{Base}=\frac{1}{2}$

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.

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

$AC=\sqrt{(1x)^2+(2x)^2}$

$AC=\sqrt{5}x$

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

According to trigonometric function,

$\sin \theta=\frac{Perpendicular}{Hypotenuse}=\frac{1x}{\sqrt{5}x}$

$\sin \theta=\frac{1}{\sqrt{5}}$

Thus, the value of $\sin \theta$ is, $\frac{1}{\sqrt{5}}$