Given:
In a right angle triangle, two interior angles are 60° and 30°, and their opposite sides are x and 3 respectively.
To find:
The length of side x in simplest radical form with a rational denominator.
Solution:
In a right angle triangle,
![\tan \theta=\dfrac{Perpendicular}{Base}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D%5Cdfrac%7BPerpendicular%7D%7BBase%7D)
Using this formula for the given triangle, we get
![\tan 30^\circ=\dfrac{3}{x}](https://tex.z-dn.net/?f=%5Ctan%2030%5E%5Ccirc%3D%5Cdfrac%7B3%7D%7Bx%7D)
![\dfrac{1}{\sqrt{3}}=\dfrac{3}{x}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%3D%5Cdfrac%7B3%7D%7Bx%7D)
On cross multiplication, we get
![1\times x=3\times \sqrt{3}](https://tex.z-dn.net/?f=1%5Ctimes%20x%3D3%5Ctimes%20%5Csqrt%7B3%7D)
![x=3\sqrt{3}](https://tex.z-dn.net/?f=x%3D3%5Csqrt%7B3%7D)
Therefore, the length of side x in simplest radical form is
units.