Answer:
This can be proved in a number of different ways, but the simplest is to use the sine trig ratio:
[tex]sin(\theta)=\dfrac{O}{H}[/tex], where [tex]\theta[/tex] is the angle, O is the side opposite the angle and H is the hypotenuse.
Given the angle is 30°:
[tex]\implies sin(30)=\dfrac{O}{H}[/tex]
[tex]\implies \dfrac12=\dfrac{O}{H}[/tex]
[tex]\implies O=\dfrac12H[/tex]
