Question

In order to unload clay easily, the body of a dump truck must be elevated to at least 50°. The body of a dump truck that is 15 feet long has been raised to 9 feet. Will the clay pour out easily? Show your work and draw a diagram to support your answer.

Please include the following:

• A diagram



• The trig equation you are solving and the steps you take to solve it.



• An answer in the context of the problem.
_________ (Yes or No), The clay ___________ (will or will not) pour out easily when the body of the dump truck is raised to 9 feet. I know this because ______________________________________.

Answer 1

No; the angle of elevation of the front bottom of the dump truck body will be only 31°, much smaller an angle than the required 50°

Explanation:

Let the body of the truck rest upon the x-axis with the rear body at (0, 0). The front of that body is located at (15, 0). The dump body is elevated to 9 ft.

We thus have a right triangle with base 15 ft and height 9 ft, and want to know what the angle is. The angle is at (0, 0). The front of the body is at (0, 15), and when elevated that point will be located at (15, 9).

The tangent function relates the angle to the opposite side (length 9 ft) and the adjacent side (length 15 ft):

tan Ф = opp / hyp = 9 / 15 = 31 degrees.

NO: the elevation of the front of the dump truck body is only 31° approx. The clay will not easily dump from the body.