Answer:
a:
[tex]sin(\theta)=\frac{opposite}{hypotenus}[/tex]
[tex]sin(60)= \frac{a}{4\sqrt3}[/tex]
[tex](4\sqrt3)sin(60)= a[/tex]
[tex](4\sqrt3)(\frac{\sqrt3}{2})= a[/tex]
[tex]6= a[/tex]
b:
the answer choices all have the same value for b, so I dont have to solve for b at all.
[tex]b=6\sqrt2[/tex]
c:
[tex]cos(\theta)=\frac{adjacent}{hypotenus}[/tex]
[tex]cos(60)= \frac{c}{4\sqrt3}[/tex]
[tex](4\sqrt3)cos(60)= c[/tex]
[tex](4\sqrt3)(1/2)= c[/tex]
[tex]2\sqrt3= c[/tex]
d:
d is inside a 45-45-90 triangle. Therefore, side a and d must be of the same length.
[tex]d=a[/tex]
[tex]d=6[/tex]