4. A customer wants to make a teepee in his backyard for his children. He plans to use lengths of PVC plumbing pipe for the supports on the teepee, and he wants the teepee to be 12 feet across and 8 feet tall (see figure). How long should the pieces of PVC plumbing pipe be?
How many corners is this so-called teepee (or tipi) supposed to have? Is it pyramidal or does it have two parallel triangular sides?
A traditional native American tipi is conical. That does not appear to be what your problem is about.
I think I got it, but thank you very much:)
To determine the length of PVC plumbing pipes needed for the teepee supports, we can use a bit of geometry. The teepee is essentially a cone shape, with the PVC pipes forming the supports for the sides.
To find the length of the PVC pipes, we need to calculate the slant height of the cone, which is the distance from the top of the cone to any point on the edge of the base.
First, let's find the slant height using the Pythagorean theorem. The slant height (l) can be found by:
l = sqrt(r^2 + h^2)
Where r is the radius of the teepee (half of the diameter) and h is the height of the teepee.
In this case, the radius is 12 feet / 2 = 6 feet, and the height is 8 feet.
l = sqrt(6^2 + 8^2)
l = sqrt(36 + 64)
l = sqrt(100)
l = 10 feet
So, the slant height of the teepee cone is 10 feet.
Since the PVC pipes will form the supports along the edges, they need to reach from the ground to the top of the cone. Thus, the length of the PVC plumbing pipe needed for the supports will be equal to the slant height.
Therefore, the length of the PVC plumbing pipes should be 10 feet each.