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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?

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 t class=

Verified Answer :

carlosego

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

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

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