Question

Find a when c=38 please help this is geometry

Answer 1

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, $sin(60) = \frac{a}{c}$
Now, sin(60) is an exact value, and you should try to remember that sin(60) can also be rewritten as $\frac{\sqrt{3}}{2}$

So, to find a, $c \cdot sin(60) = 38 \cdot \frac{\sqrt{3}}{2}$
$a = 19\sqrt{2}$