Question

Find the length of side x in the simplest radical form with a rational denominator​

Answer 1

Answer:

Step-by-step explanation:

Recognize that this is a 30-60-90 triangle.  

Write and solve an equation of ratios:

 x         1

------ = ------- (which is the tangent of 30°)

√2       √3  

Then √3*x = √2, and so:

       √2

x = ----------

        √3

Rationalize this as follows:  

      √2*√3        √6

x = ------------- = ------

            3-            3

Answer 2

Answer: 10√3 / 3

Step-by-step explanation:

cos 30 = 5 / x

x = 5 / cos 30

= 5 / √3 / 2

= 10 √3

= 10√3 / 3