ANSWER
The lengths of the legs of the triangle are 6.06 yards and 3.6 yards.
EXPLANATION
First, let us make a sketch of the problem:
To find the length of the legs, we have to apply trigonometric ratios SOHCAHTOA.
We have that:
[tex]\sin (60)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]From the diagram:
[tex]\begin{gathered} \sin (60)=\frac{x}{7} \\ \Rightarrow x=7\cdot\sin (60) \\ x\approx6.06\text{ yds} \end{gathered}[/tex]We also have that:
[tex]\sin (30)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]From the diagram:
[tex]\begin{gathered} \sin (30)=\frac{y}{7} \\ \Rightarrow y=7\cdot\sin (30) \\ y=3.5\text{ yds} \end{gathered}[/tex]The lengths of the legs of the triangle are 6.06 yards and 3.5 yards.
