30-60-90 right triangles:
scale factors for sides opposite 30, 60 and 90 degree angles are 1: sqrt(3): 2
7) side opposite 60 degree angle is 5*sqrt(3) which is sqrt(3) times side opposite 30 degree angle, so b = 5.
hypotenuse is equal to 2 times the side opposite the 30 degree angle, so a = 10.
8) side opposite 60 degree angle is 9 which is sqrt(3) times side opposite 30 degree angle so y = 9/sqrt(3) = 3*sqrt(3). hypotenuse equals 2 * 3 * sqrt(3) = 6 * sqrt(3)
9) side opposite 60 degree angle is 11 * sqrt(3), so side opposite 30 degree angle is 11*sqrt(3)/sqrt(3) = 11. hypotenuse is equal to 2 * 11 = 22.
10) hypotenuse is 39. Side opposite 30 degree angle is half of that or 19.5. Side opposite 60 degree angle is 19.5*sqrt(3).
