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√(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√(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√(3) \\ \boxed{b=5√(3)} \end{gathered}`