Question

the height of the pyramid is 21.5 meters. use the interactives to review applying the pythagorean theorem to determine unknown side lengths in right triangles in real - world problems in three dimensions. question 1 a camping tent is in the shape of a square pyramid. the sides of the tent are 15 yards and the edge length is 18 yards. find the slant height of the triangle. round the answer to the nearest tenth. the slant height of the triangle is yards. check answer remaining attempts: 3

Explanation:

Step1: Find half of the base length

The base of the tent is a square with side length \(15\) yards. Half of the base length \(a=\frac{15}{2}=7.5\) yards.

Step2: Apply the Pythagorean theorem

The slant height \(l\) (the hypotenuse of the right - triangle formed by half of the base and the slant height) and the edge length of the triangular face of the pyramid. Let the slant height be \(l\). Using the Pythagorean theorem \(l=\sqrt{18^{2}-7.5^{2}}\).
First, calculate \(18^{2}=324\) and \(7.5^{2}=56.25\). Then \(18^{2}-7.5^{2}=324 - 56.25=267.75\).
So \(l=\sqrt{267.75}\approx16.4\)

Answer:

\(16.4\)