Question

Find each length:

Answer 1

Answer:

The length of the longer leg is $7\sqrt{3}\ units$

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

$sin(60^o)=\frac{AC}{AB}$ ----> by SOH (opposite side divided by the hypotenuse)

Remember that

$sin(60^o)=\frac{\sqrt{3}}{2}$

$AB=14\ units$

substitute the given values

$\frac{\sqrt{3}}{2}=\frac{AC}{14}$

$AC=7\sqrt{3}\ units$