Answer: [tex]\frac{10}{\sqrt{3}}[/tex]
This is equivalent to [tex]\frac{10\sqrt{3}}{3}[/tex]
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Explanation:
To get the first value mentioned above, we simply divide the long leg (10) over the square root of 3.
This is due to the fact that if x is the short leg, then x*sqrt(3) is the long leg. We go in reverse of this process to go from long leg to short leg.
The expression [tex]\frac{10}{\sqrt{3}}[/tex] is the same as [tex]\frac{10\sqrt{3}}{3}[/tex] after we multiply top and bottom by sqrt(3) to rationalize the denominator.
Side notes:
- This entire process only applies to 30-60-90 triangles.
- The hypotenuse of a 30-60-90 triangle is twice as long as the short leg, so the hypotenuse is [tex]2x = 2*\frac{10\sqrt{3}}{3} = \frac{20\sqrt{3}}{3}[/tex] units long.
- You could use the tangent ratio to help isolate x. You would either say tan(30) = x/10 or tan(60) = 10/x as the first equation to set up.
