Question

Help with Trigonometry/Geometry! #1-3

Answer 1

Whew this is a doozy. I'm assuming that that is an isosceles triangle and that drawing an altitude down the center cuts the base directly in half. It also creates 2 right congruent triangles. So #1: The altitude is 13, which is the height of the right triangle, and the base of one of those right triangles is 19.3 (divide the 38.6 in half). Now you use the tangent ratio to get tan A = 13/19.3  Doing that math in degrees on your calculator with your inverse button, you will get that the angle measure is 33.9 or 34.0 degrees. #2: use the same angle of repose and the new height of 10. Use the tan ratio again to get that half the base is 14.8 and the whole base is double that at 29.7 rounded. #3 is the difficult one. The angle of repose is 30, the height is 11 so you need the tan ratio again to find half the base which is 19.05. Now in order to find out the cost per cubic yard, you have to convert feet to yards and use the volume formula for a cone. And I'm out of room here.