Question

30-60-90 triangle find the measure of the missing two sides for each figure below leave answering rationalized or simple form

Answer 1

According to the figure, we have a special right triangle where its hypotenuse is 2k, and the missing leg is k.

We know that the second leg is 15, so

`\begin{gathered} \sqrt[]{3}\cdot k=15 \\ k=\frac{15}{\sqrt[]{3}} \end{gathered}`

Let's rationalize

`k=\frac{15}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{15\sqrt[]{3}}{3}=5\sqrt[]{3}`

Where k is the missing leg.

So, the hypothenuse would be 2k, which is

`2\cdot5\sqrt[]{3}=10\sqrt[]{3}`