Question

a tipi (or teepee) was historically used by native americans in the great plains for homes and ceremonies. today, tipis, such as the one described below, are primarily used for cultural events and hunting. the floor of the tipi is in the shape of a circle with a radius of 13 feet. the vertical height from the center of the floor to the point where the poles cross at the top is 27 feet. each pole goes from the outside edge of the circular floor through the point where the poles cross at the top center and extends an additional 5 feet beyond the intersection point. what is the length of one pole, to the nearest whole foot? 45 ft 32 ft 29 ft 35 ft

Explanation:

Step1: Apply Pythagorean theorem

We can consider a right - triangle formed. The vertical height from the center of the floor to the top of the tipi is \(h = 27\) feet and the radius of the circular floor is \(r=13\) feet. Each pole extends 5 feet beyond the intersection point. The length of the pole from the edge of the circular floor to the top of the tipi forms the hypotenuse of a right - triangle. The vertical side of the right - triangle is \(h = 27\) feet and the horizontal side is \(r = 13\) feet. First, find the length from the edge of the floor to the top of the tipi using the Pythagorean theorem \(a=\sqrt{r^{2}+h^{2}}\), where \(r = 13\) and \(h = 27\).
\[a=\sqrt{13^{2}+27^{2}}=\sqrt{169 + 729}=\sqrt{898}\approx29.97\]

Step2: Add the extra 5 - foot length

The total length of the pole \(L=a + 5\). Substituting the value of \(a\approx29.97\), we get \(L\approx29.97+5=34.97\approx35\) feet.

Answer:

35 ft