Answer:
[tex] \frac{ \sqrt{6} }{3} [/tex]
Step-by-step explanation:
To find side x , since it the shortest side. Divide the second longest side by sqr root of 3.
Why?
This is a 30-60-90 triangle so that means the second longest side will be sqr root of 3 times more than the shortest side
[tex] \sqrt{2} \div \sqrt{3} [/tex]
[tex] \frac{ \sqrt{2} }{1} \times \frac{1}{ \sqrt{3} } = \frac{ \sqrt{2} }{ \sqrt{3} } [/tex]
RATIONALIZE the denominator
[tex] \frac{ \sqrt{2} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{ \sqrt{6} }{3} [/tex]
Sqr root of 6 over 3 is the answer.
This section is extra If you want to.
Since the longest side is twice the shortest side, the longest side is
[tex] \frac{2 \sqrt{6} }{3} [/tex]
Let proof
using pythagorean theorem,
[tex]( \frac{ \sqrt{6} }{3} ) {}^{2} + (\sqrt{2} ) {}^{2} [/tex]
[tex] \frac{6}{9} + 2 = \frac{24}{9} [/tex]
[tex] \sqrt{ \frac{ {24} }{9} } = \frac{2 \sqrt{6} }{3} [/tex]
So it is right.