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?
a. 4.82 ft
c. 3.48 f
b. 2.41 ft
d. 5.36 ft
To determine the width of the tent, we need to find the base of the triangular prism.
Since the height of the man is given as 6 ft, this will be the height of the triangular prism.
Let's assume the width of the tent as x.
To find the base of the triangular prism, we need to determine the length of the slope.
Using trigonometry, we can calculate the length of the slope using the formula:
length = height / sin(angle)
In this case, the angle is given as 68.1° and the height is given as 6 ft.
length = 6 / sin(68.1°) ≈ 6 / 0.923 ≈ 6.5 ft
Since we have the length of the slope, we can use it to calculate the width of the tent.
width = 2 * length = 2 * 6.5 ≈ 13 ft
However, this is the width of the base of the triangular prism.
Since the tent is assumed to have the shape of a triangular prism, the width can be considered as the width of the base.
Hence, the correct width of the tent to accommodate a 6-ft tall man standing up is approximately 13 ft.
None of the given options (a, b, c, d) match the calculated value.