Ratios of special triangles

[carrieandgeoff]

Find the length of side x in simplest radical form with a rational denominator. 30-60-90 triangle. The short side across from the 30 degree angle is labeled x, the base across from the 60 degree angle is labeled 2, the hypotenuse is not labeled at all.

 

[Steven G]

You have the length of the two legs (one is in terms of x which you want to solve for.) Can you think of any trig functions that just uses the legs? If yes then use one of them. If not then go back and study the definitions of your trig functions.

 

[pka]

To do this question you need these:
\(\tan\left(\dfrac{\pi}{6} \right)=\dfrac{x}{2}\)
\(\tan\left(\dfrac{\pi}{3} \right)=\dfrac{2}{x}\)
All you need is the value of \(x\).
The length of the hypotenuse is \(\sqrt{2^2+x^2}\).