Question 212133
This triangle is a 30-60-90 triangle because one of the legs doubled is the hypotenuse.

Remember similar triangles have equal proportions.

Let x be the hypotenuse, y the leg half of x, and z the other leg.

sqrt(3)/2=z/x
x=z+6 so

sqrt(3)/2 = z/(z+6)
Solve the proportion by cross multiplying to find z.

z is (sqrt(3)*6)/(2-sqrt(3)). Approximation z = 38.8

x is approximately 44.8 since you add 6 to z.

y is half of x so y = 22.4


Test these numbers with the Pythagorean theorem.