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, \(\frac{1}{\sqrt{5}}\)
