Question

Daniel is planning to go camping, but he lost the pole that supports the middle point of the tent. A cross-section of the tent is shown below. The base of the tent measures 96 inches wide, and the length from the top point of the tent to the corners of the base is 102 inches.

Answer 1

The length of the center pole needed would be:

c^2=e^2-(d/2)^2

c=center height, e=edge length, and d=diagonal of base.

The diagonal of the base is:

d^2=96^2+96^2

d^2=18432
 
We want half of the diagonal squared so: 

(d/2)^2=d^2/4 and given that d^2=18432

(d/2)^2=4608

We were given that e=102 so now we can solve for c:

c^2=e^2-(d/2)^2 becomes:

c^2=10404-4608

c^2=5796

c=√5796 inches

c≈76.13 inches  (to nearest hundredth of an inch)

Answer 2

90 inches. It is simple pythag. The Hyp is 102, the adj is 96/2=48 and the opposite is what you solve for 102^2-48^2=90^2