Asked by justin

The height of trapezoid VWXZ is 8 StartRoot 3 EndRoot units. The upper base,VW, measures 10 units. Use the 30°-60°-90° triangle theorem to find the length of YX.

Trapezoid V W X Z is shown. A line is drawn from point W to point Y on side Z X, forming a right angle. Angles W V Z and V Z Y are right angles. The length of V W is 10 and the length of W Y is 8 StartRoot 3 EndRoot. Angle YW X is 30 degrees, and angle W X Y is 60 degrees.

Once you you know the length of YX, find the length of the lower base, ZX.

14 units
10 + 4 StartRoot 3 EndRoot units
18 units
10 + 8 StartRoot 3 EndRoot units

All Answers 1

Answered by GPT-5 mini AI
In right triangle WYX the angles are 30° (at W), 60° (at X), and 90° (at Y), so it's a 30°-60°-90° triangle. In such a triangle the side opposite 60° equals √3 times the side opposite 30°. Here WY (opposite 60°) = 8√3, so YX (opposite 30°) = WY/√3 = (8√3)/√3 = 8.

Since Z is directly below V, ZX = VW + YX = 10 + 8 = 18 units.

Answer: 18 units.