MHB 30-60-90 triangle side lengths

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In a 30-60-90 triangle with a long leg measuring 8, the short leg is represented as x, and the hypotenuse as 2x. The relationship between the sides indicates that the long leg equals x times the square root of 3. By setting up the equation x times the square root of 3 equal to 8, the value of x is calculated as 8 divided by the square root of 3, which simplifies to 8 times the square root of 3 over 3. Consequently, the short leg measures 8 times the square root of 3 over 3, and the hypotenuse is 16 times the square root of 3 over 3.
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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.
 
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jimhayes said:
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 $\displaystyle{2\frac{8 \cdot \sqrt{3}}{3}=\frac{16 \cdot \sqrt{3}}{3}}$
 
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