Answer : The correct option is, (A) 30°
Step-by-step explanation :
As we know that:
[tex]\cos 30^o=\frac{\sqrt{3}}{2}[/tex] ........(1)
According to trigonometric function,
[tex]\cos \theta=\frac{Base}{Hypotenuse}[/tex] .........(2)
By comparing 1 and 2, we can say that:
[tex]\cos 30^o=\frac{\sqrt{3}}{2}=\frac{Base}{Hypotenuse}[/tex]
Now we have to determine the value of perpendicular by using Pythagoras theorem.
[tex](Hypotenus)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](2)^2=(Perpendicular)^2+(\sqrt{3})^2[/tex]
[tex]4=(Perpendicular)^2+3[/tex]
[tex](Perpendicular)^2=4-3[/tex]
[tex](Perpendicular)^2=1[/tex]
[tex]Perpendicular=1[/tex]
Now we have to determine the value of [tex]\sin \theta[/tex].
According to trigonometric function,
[tex]\sin \theta=\frac{Perpendicular}{Hypotenuse}[/tex]
[tex]\sin \theta=\frac{1}{2}[/tex]
At [tex]\theta =30^o[/tex]
[tex]\sin 30^o=\frac{1}{2}[/tex]
Hence, the value of [tex]\theta[/tex] is [tex]30^o[/tex]
