Answer: The last option.
Step-by-step explanation:
The triangle shown in the figure attached is a right triangle.
1. You can calculate the lenght a as following:
[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
[tex]opposite=a\\hypotenuse=6in\\\alpha=30\°[/tex]
Substitute values and solve for a. Then, you obtain:
[tex]sin(30\°)=\frac{a}{6in}\\a=6in*sin(30\°)\\a=3in[/tex]
2. You can calculate the lenght b as following:
[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]
[tex]adjacent=b\\hypotenuse=6in\\\alpha=30\°[/tex]
Substitute values and solve for b. Then, you obtain:
[tex]cos(30\°)=\frac{b}{6in}\\b=6in*cos(30\°)[/tex]
[tex]b=3\sqrt{3}in[/tex]
