Question

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

60
х
309
2

Answer 1

`(2)/(3) √(3)`

Explanation:

We know this triangle has angles 30, 60, and 90 degrees. Triangles with these angles have a special relationship on the sides.

The side opposite to the 90 degree angle is 2 times of x.

The side opposite to the 60 degree angle is
`√(3)` multiplied x.

We know the side opposite to 60 degree angle is 2, so x would be

`(2)/(√(3))`

However, we can't have an irrational number in the demoninator so we multiply the fractice by root 3 over root 3:

`(2)/(√(3)) * (√(3))/(√(3))`

which gives us
`(2)/(3) √(3)`