Question

The height of trapezoid VWXZ is 8(square 3) units. The upper base,VW, measures 10 units. Use the 30°-60°-90° triangle theorem to find the length of YX.
What is the length of the lower base, ZX?

Answer 1

30 ° - 60 ° - 90 ° triangle theorem states that:

Base of the triangle is:

$b = x$

The height of the triangle is:

$h = \sqrt{3} x$

The hypotenuse of the triangle is:

$H = 2x$

Therefore, we have then that the height is:

$\sqrt{3} x = 8\sqrt{3}$

From where we conclude that the value of x is:

$x = 8$

Thus, the length of the base is:

$YX = x = 8$

Finally, the length ZX is:

$ZX = VW + YX$

Substituting values:

$ZX = 10 + 8\\ZX = 18$

Answer:

the length of the lower base, ZX is:

$ZX = 18$

option 3

Answer 2

Using a regular 1 - sqrt(3) - 2 triangle, we can use proportions. 8 sqrt(3) / sqrt(3) = 8. Then, you use the ten from the rectangle side, getting us the answer: 18. Hoped this helped!!!