Final answer:
To find the length of YX, we use the 30°-60°-90° triangle theorem. The length of YX is 16/3 units. To find the length of ZX, we subtract the length of YX from VW.
Step-by-step explanation:
To find the length of YX, we can use the 30°-60°-90° triangle theorem. In this theorem, the length of the hypotenuse (opposite the 90° angle) is twice the length of the shorter leg (opposite the 30° angle). So, if the height of trapezoid WWXZ is 8/3 units, the length of WX (the shorter leg) is 8/3 units. Then, the length of YX (the hypotenuse) is twice the length of WX, which is 2 * (8/3) = 16/3 units.
To find the length of ZX, we can use the fact that the upper base, VW, measures 10 units. Since WX is the shorter leg of the 30°-60°-90° triangle, VW is equal to the sum of YX and ZX. Therefore, ZX = VW - YX. Substituting the values, ZX = 10 - (16/3) = (30 - 16)/3 = 14/3 units.