Given:
The figure of a right triangle.
To find:
The value of [tex]\sin(30^\circ)[/tex].
Solution:
We know that, the sides of 30°-60°-90° right triangle are [tex]x,x\sqrt{3},2x[/tex] opposite to the angles 30°, 60°, 90° respectively.
Opposite side of 90° is 9.
[tex]2x=9[/tex]
[tex]x=\dfrac{9}{2}[/tex]
[tex]x=4.5[/tex]
So, opposite side of 30° is 4.5.
In a right triangle:
[tex]\sin\theta = \dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\sin (30^\circ)= \dfrac{4.5}{9}[/tex]
[tex]\sin (30^\circ)= \dfrac{1}{2}[/tex]
Therefore, the correct option is A.
