Use the image to answer the question.
An illustration shows a square pyramid with labeled parts. The front and left faces of the pyramid and base are visible. The back and right faces are not visible. The back and right base edges are not visible but their position is indicated by a dashed line. The left base edge shows a length of 16 feet. A dotted line extends from the interior of the vertex straight down to the center of the base and shows a height of 15. A right angle is indicated where the dotted height line meets the base.
Find the slant height of the square pyramid.
To find the slant height of the square pyramid, we can use the Pythagorean Theorem.
First, let's label the parts of the pyramid that we know:
The left base edge is labeled as 16 feet.
The height from the vertex to the center of the base is labeled as 15 feet.
Since the height of the pyramid forms a right angle with the base, we can use the Pythagorean Theorem to find the slant height.
Let's call the slant height "s". We can set up the equation:
s^2 = 16^2 + 15^2
s^2 = 256 + 225
s^2 = 481
Taking the square root of both sides:
s = √481
Therefore, the slant height of the square pyramid is approximately 21.93 feet.