A camp tent is shaped like a triangular prism. If the sides slope at 68.1° above the ground, how wide must the tent be to accommodate a 6-ft tall man standing up?
To find the width of the tent, we need to use the properties of a triangular prism.
Let's consider the triangular base of the prism. The base forms an isosceles triangle, with two equal sides and one base. The angle formed between the base and one of the equal sides is 68.1°.
The height of the triangular prism is given as 6 ft, which means the height forms the hypotenuse of a right triangle on the base. Let's call one of the equal sides of the base x.
Using trigonometry, we can find the width of the tent by finding the length of the base. We can set up the following equation:
sin(68.1°) = 6 / x
To solve for x, we can rearrange the equation:
x = 6 / sin(68.1°)
Using a calculator, we can find:
x ≈ 6 / 0.923
x ≈ 6.5 ft
Therefore, the tent must be approximately 6.5 ft wide to accommodate a 6-ft tall man standing up.