Question

I need to find side x of this 30 60 90 triangle i think with special right triangle methods

Answer 1

This is a 30-60-90 triangle and we can apply rules to easily identify the hypotenuse of this triangle, which is denoted by x.

The length of the longer side of the triangle is given in the problem. To solve the hypotenuse of this triangle, let's solve first for the length of the shorter side of the triangle.

The shorter side can be solved by just dividing the length of the longer side by the square root of 3. Hence, we have

$short=\frac{4}{\sqrt[]{3}}$

Since we already have the values for the length of the shorter side and longer side, we can solve for the hypotenuse using the Pythagorean theorem.

$\begin{gathered} c=\sqrt[]{a^2+b^2} \\ c=\sqrt[]{4^2+(\frac{4}{\sqrt[]{3}})^2} \\ c=\sqrt[]{16+\frac{16}{3}} \\ c=\sqrt[]{\frac{64}{3}} \\ c=\frac{8}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ c=\frac{8\sqrt[]{3}}{3} \end{gathered}$

Hence, the value of hypotenuse for this right triangle is

$x=\frac{8\sqrt[]{3}}{3}$