Answer:
The length of the longer leg is [tex]7\sqrt{3}\ units[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In any triangle:
The shortest side is always opposite the smallest interior angle. The longest side is always opposite the largest interior angle
so
The longer leg is AC
we have
[tex]sin(60^o)=\frac{AC}{AB}[/tex] ----> by SOH (opposite side divided by the hypotenuse)
Remember that
[tex]sin(60^o)=\frac{\sqrt{3}}{2}[/tex]
[tex]AB=14\ units[/tex]
substitute the given values
[tex]\frac{\sqrt{3}}{2}=\frac{AC}{14}[/tex]
[tex]AC=7\sqrt{3}\ units[/tex]
