The triangle with legs x and y is a 30 - 60 - 90 triangle. The patterns of the legs are as follows:
short leg (opposite 30 degree angle) = 1 unit
long leg (opposite 60 degree angle) √3 units
hypotenuse = 2 units.
The pattern is that we double the short leg to get the hypotenuse, or, we go in reverse and take half the hypotenuse to get the short leg.
In the picture we are told the hypotenuse is 16. That makes the short leg as 8, which is x in the picture.
Now we find the long leg and multiply it by √3. This gives us 8√3., the side y.
Thus, x = 8 and y = 8√3.
