41,560 views
19 votes
19 votes
This is a 30-60-90 triangle.What is the measure of x?Rationalize the denominator.x = [?]?12

This is a 30-60-90 triangle.What is the measure of x?Rationalize the denominator.x-example-1
User Nicorr
by
2.7k points

1 Answer

20 votes
20 votes

The value of x is:


x=4\sqrt[]{3}

To solvbe this, we need to use the tan function. The 60º is at the top left of the triangle, and the 30º angle is on the bottom right.

Then we know, the angle bottom right = 30º, the opposite leg = x and the adjacent leg = 12

The trignometrical function that relates those 3 things is tangent:


\tan (\theta)=\frac{\text{opposite leg}}{\text{ adjacent leg}}

In this case:


\begin{gathered} \tan (30º)=(x)/(12) \\ x=12\cdot\tan (30º) \end{gathered}

Thus:


\tan (30º)=\frac{1}{\sqrt[]{3}}\Rightarrow x=12\cdot\tan (30º)=\frac{12}{\sqrt[]{3}}

Now we need to rationalize the answer. To do it, we multiply and divide by the denominator:


x=\frac{12}{\sqrt[]{3}}*\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{12\sqrt[]{3}}{3}=4\sqrt[]{3}^{}

And that's the answer

User Misha Moroshko
by
2.6k points