MHB 30-60-90 triangle side lengths

[jimhayes]

I have a 30-60-90 triangle with the length of 8 for the long leg. I am trying to find the lengths of the other two legs. I believe the short leg is x, and hypotenuse is 2x, and the long leg is x times the \sqrt{3}. I put x times \sqrt{3}=8 although I am not sure how to do this formula to find the value of x. I also don't have a calculator with square root functions.

 

[mathmari]

I have a 30-60-90 triangle with the length of 8 for the long leg. I am trying to find the lengths of the other two legs. I believe the short leg is x, and hypotenuse is 2x, and the long leg is x times the \sqrt{3}. I put x times \sqrt{3}=8 although I am not sure how to do this formula to find the value of x. I also don't have a calculator with square root functions.

short leg: $x$
hypotenuse: $2x$
long leg: $x \cdot \sqrt{3}$

It is given that the long leg is $8$, so $\displaystyle{x \cdot \sqrt{3}=8 \Rightarrow x=\frac{8}{\sqrt{3}}=\frac{8 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}=\frac{8 \cdot \sqrt{3}}{3}}$

So, the short leg is $\displaystyle{\frac{8 \cdot \sqrt{3}}{3}}$ and the hypotenuse is $\displaystyle{2\frac{8 \cdot \sqrt{3}}{3}=\frac{16 \cdot \sqrt{3}}{3}}$