Question

Hi can you help me find the correct answer to this?

Answer 1

In this problem, we want to apply special right triangles.

We will take a close look at the 30-60-90 triangle:

When working with this special right triangle, we can apply the following ratio for the legs and hypotenuse:

$\begin{gathered} \text{ short leg}:\text{ long leg}:\text{ hypotenuse} \\ \\ x:x\sqrt{3}:2x \end{gathered}$

As long as we know one of the three legs, we can find the missing legs as well.

We are given the following diagram:

It looks like we were given the hypotenuse. Using our ratio above, we see:

$\begin{gathered} x:x\sqrt{3}:2x \\ \\ a:b:10 \end{gathered}$

Let 10 be equal to the hyptonuse length from the ratio.

$10=2x$

Solve for x by dividing by 2:

$5=x$

Since know a = x,

$\boxed{a=5}$

We can find b the same way:

$\begin{gathered} b=x\sqrt{3} \\ \boxed{b=5\sqrt{3}} \end{gathered}$