Since we have a right angle triangle, we can use a trigonometric ratio to help us solve for an unknown side.
Given that c = 38, we need to solve for a.
Since c is the hypotenuse, we can choose to use the sine or cosine ratio.
Let's use the sine ratio; that means our angle of interest is 60°
So, [tex]sin(60) = \frac{a}{c}[/tex]
Now, sin(60) is an exact value, and you should try to remember that sin(60) can also be rewritten as [tex]\frac{\sqrt{3}}{2}[/tex]
So, to find a, [tex]c \cdot sin(60) = 38 \cdot \frac{\sqrt{3}}{2}[/tex]
[tex]a = 19\sqrt{2}[/tex]
