A camp tent is shaped like a triangluar prisim. If the sides slope is 68.1 degree above the ground, how wide must the tent be to accommodate a 6-foot tall man standing up?
To solve this problem, we need to use trigonometry. Let's denote the width of the tent as W.
First, we need to find the height of the triangular prism. We know that the man's height is 6 feet, so this will be the height of the triangular prism as well.
Next, we can calculate the length of the triangular base of the prism. To do this, we can imagine drawing a horizontal line from the top of the triangular prism to the ground. This line will be parallel to the base of the triangular prism and will cut the triangle into two right triangles. The angle between the line and the ground is 68.1 degrees.
Now, we can use trigonometry to find the length of the base. We have a right triangle with the angle 68.1 degrees and the opposite side 6 ft (height of the prism), and we want to find the adjacent side (base of the prism). We can use the tangent function:
tan(68.1°) = opposite / adjacent
tan(68.1°) = 6 ft / W
To isolate W, we can rearrange the equation:
W = 6 ft / tan(68.1°)
Using a calculator, we find that the width of the tent must be approximately 2.145 ft.