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 the 30°-60°-90° triangle theorem, we can find that the area of the trapezoid is 242.48 unit².

What is the trapezoidal?

The polygon has four sides and four vertices. In this a pair of opposite sides are parallel. Trigonometry deals with the side and angles of the triangle.

Area of trapezoidal

$\rm Area\ of\ trapezoid = \dfrac{1}{2} (sum\ of\ parallel\ sides) * height$

Given

VW║ZYXVW = YZ = 10 units.

WY = 8√3∠x = 60°.

To find

The area of the trapezoid.

In ΔXYW

$\begin{aligned} \rm tan\ \theta\ &= \dfrac{Perpdicular}{Base}\\\rm tan 60^{o} &= \rm \dfrac{8\sqrt{3} }{XY} \\\rm XY &= 8\\\end{aligned}$

Then XZ = XY + YZ = 10 + 8 = 18 unit.

Then the area of the trapezium will be

$\rm Area\ of\ trapezium = \dfrac{1}{2} (sum\ of\ parallel\ side)*\ height\\\\Area\ of\ trapezium = \dfrac{1}{2} (VW + XZ)* WY\\\\Area\ of\ trapezium = \dfrac{1}{2} (18+10)*10\sqrt{3} \\\\Area\ of\ trapezium = 242.48$

Thus, the area of the trapezoid is 242.48 unit².

More about the trapezoid link is given below.

https://brainly.com/question/4758162