Question

the height of trapezoid vwxz is $8\sqrt{3}$ units. the upper base, $\overline{vw}$, measures 10 units. use the $30^\circ$-$60^\circ$-$90^\circ$ triangle theorem to find the length of $\overline{yx}$. once you you know the length of $\overline{yx}$, find the length of the lower base, $\overline{zx}$. \bigcirc 14 units \bigcirc $10 + 4\sqrt{3}$ units \bigcirc 18 units \bigcirc $10 + 8\sqrt{3}$ units

Explanation:

Step1: Identify 30-60-90 triangle sides

In a 30°-60°-90° triangle, the sides follow the ratio: shorter leg : longer leg : hypotenuse = $1:\sqrt{3}:2$. Here, the height $WY = 8\sqrt{3}$ is the longer leg (opposite 60° angle). Let the shorter leg $YX = x$.
$$\sqrt{3}x = 8\sqrt{3}$$

Step2: Solve for length of $\overline{YX}$

Divide both sides by $\sqrt{3}$:
$$x = \frac{8\sqrt{3}}{\sqrt{3}} = 8$$

Step3: Calculate lower base $\overline{ZX}$

The lower base is the sum of the upper base and $\overline{YX}$:
$$ZX = VW + YX = 10 + 8$$

Answer:

18 units