Question

A trapezoid is shown below.28 feet12 feet.HINT. HOW DO I ANDTHIS HORIZONTALDISTANCE?36 feetCalculate the measure of angle x, to the nearesttenth of a degree.

Answer 1

As you can see in the picture given in the exercise, the trapezoid can be divided into two figures: a rectangle and a Right triangle.

Let be "b" the base of the triangle (the horizontal distance indicated in the exercise). You can set up that:

`\begin{gathered} b=36ft-28ft \\ b=8ft \end{gathered}`

Now you can use the following Inverse trigonometric function to find the measure of the angle "x":

`x=\sin ^(-1)((opposite)/(hypotenuse))`

In this case:

`\begin{gathered} opposite=b=8 \\ hypotenuse=12 \end{gathered}`

Then, substituting values and evaluating, you get:

`\begin{gathered} x=\sin ^(-1)((8)/(12)) \\ \\ x\approx41.8\degree \end{gathered}`

The answer is:

`x\approx41.8\degree`