Question

the height of trapezoid vwxz is 8√3 units. the upper base, vw, measures 10 units. use the 30 - 60 - 90 triangle theorem to find the length of yx. once you know the length of yx, find the length of the lower base, zx. 14 units 10 + 4√3 units 18 units 10 + 8√3 units

Explanation:

Step1: In 30 - 60 - 90 triangle

In right - triangle $YWX$, if the height (opposite the 30° angle) is $h = 8\sqrt{3}$, then the side opposite the 60° angle $YX$ can be found using the ratio of sides in a 30 - 60 - 90 triangle. The ratio of the sides of a 30 - 60 - 90 triangle is $1:\sqrt{3}:2$. If the side opposite 30° is $a$, the side opposite 60° is $a\sqrt{3}$ and the hypotenuse is $2a$. Here, if the side opposite 30° is $8$, then the side opposite 60° ($YX$) is $8$.

Step2: Find lower base

The lower base $ZX=ZY + YX$. Since $ZY = 10$ and $YX = 8$, then $ZX=10 + 8=18$.

Answer:

18 units