Question

Find the length of side xx in simplest radical form with a rational denominator.
30°
60°
x
7

Answer 1

A 30°–60°–90° triangle has side ratios
short leg : long leg : hypotenuse = 1 : √3 : 2,
where the short leg is opposite 30° and the long leg is opposite 60°.

If the given 7 is the side opposite 60° (the √3·short leg), then
short leg = 7/√3 = (7√3)/3,
so x = 7√3/3.

(If instead 7 were the hypotenuse then the short leg would be 7/2 and the other leg 7√3/2.)