Answer:
[tex]\large\boxed{B.\ \dfrac{1}{2}}[/tex]
Step-by-step explanation:
Look at the picture.
We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.
Therefore
[tex]b\sqrt3=3.5\sqrt{x}[/tex] divide both sides by √3
[tex]b=\dfrac{3.5\sqrt{x}}{\sqrt3}[/tex]
[tex]a=2b\to a=2\cdot\dfrac{3.5\sqrt{x}}{\sqrt3}=\dfrac{7\sqrt{x}}{\sqrt3}[/tex]
The sine is:
[tex]\sine=\dfrac{opposite}{hypotenuse}[/tex]
We have
[tex]opposite=\dfrac{3.5\sqrt{x}}{\sqrt3}\\\\hypotenuse=\dfrac{7\sqrt{x}}{\sqrt3}[/tex]
Substitute:
[tex]\sin30^o=\dfrac{3.5\sqrt{x}}{\sqrt3}:\dfrac{7\sqrt{x}}{\sqrt3}=\dfrac{3.5\sqrt{x}}{\sqrt3}\cdot\dfrac{\sqrt3}{7\sqrt{x}}\\\\\text{cancel}\ \sqrt{x}\ \text{and}\ \sqrt3\\\\\sin30^o=\dfrac{3.5}{7}=\dfrac{35}{70}=\dfrac{1}{2}[/tex]
