Question

Given a planar trapezoid ABCD whose height is BE. It is known that AB = 8cm A = 60 *, find the height ofthe trapezoid.

Answer 1

Given the trapezoid:

To solve for the height of the trapezoid, we use the trigonometric ratio.

From the trigonometric ratios,

`\sin\theta=(opposite)/(hypotenuse)`

In this case, in the triangle AEB, θ is ∠A.

Thus,

`\sin A=(BE)/(AB)`

By cross-multiplying, we have

`\begin{gathered} BE=AB*\sin A \\ =8*\sin60 \\ =8*(√(3))/(2) \\ \Rightarrow BE=4√(3)\text{ cm} \end{gathered}`

Hence, the height of the trapezoid is

`4\sqrt{3\text{ }}\text{ cm}`