The sides of a 30-60-90 triangle are defined by x, 2x, and [tex]x \sqrt{3} [/tex], where 2x is the longest side and x is the shortest.
The problem tells us that the longest side is [tex] \sqrt{75} [/tex] (which is equal to 2x). We can write an equation to find x.
2x=[tex] \sqrt{75} [/tex]
Divide both sides by 2
2x/2=[tex] \sqrt{75}/2 [/tex]
x=[tex]\frac{ \sqrt{75} }{2} [/tex]
:)
