Given:
The given triangle is a right triangle.
One of the angle of the triangle is 60°
The length of the hypotenuse is 8.
The length of the side opposite to the angle 60° is x.
We need to determine the value of x.
Value of x:
The value of x can be determined using the trigonometric ratio.
Thus, we have;
[tex]sin \ \theta=\frac{opp}{hyp}[/tex]
Substituting [tex]\theta=60^{\circ}[/tex], [tex]opp=x[/tex] and [tex]hyp=8[/tex], we get;
[tex]sin \ 60^{\circ}=\frac{x}{8}[/tex]
Multiplying both sides by 8, we have;
[tex]sin \ 60^{\circ} \times 8=x[/tex]
[tex]\frac{\sqrt{3}}{2} \times 8=x[/tex]
[tex]4 \sqrt{3}=x[/tex]
Thus, the value of x is [tex]4 \sqrt{3}[/tex]
Hence, Option B is the correct answer.
