Question
The slant hight is 15 and the length is 16 right pyramid
Answers
GPT-4o mini
To find the height of a right pyramid with a slant height of 15 and a base length of 16, you can relate the slant height, the height (h), and half the base length (which is half of 16, or 8) using the Pythagorean theorem.
In a right pyramid, the slant height, the height of the pyramid, and half the length of the base form a right triangle. The relationship is given by:
\[
\text{slant height}^2 = \text{height}^2 + \left(\frac{\text{base length}}{2}\right)^2
\]
Substituting the given values:
\[
15^2 = h^2 + 8^2
\]
Calculating the squares:
\[
225 = h^2 + 64
\]
Now, isolate \(h^2\):
\[
h^2 = 225 - 64
\]
\[
h^2 = 161
\]
Now, take the square root:
\[
h = \sqrt{161} \approx 12.6886
\]
Therefore, the height of the right pyramid is approximately \(12.69\).
In a right pyramid, the slant height, the height of the pyramid, and half the length of the base form a right triangle. The relationship is given by:
\[
\text{slant height}^2 = \text{height}^2 + \left(\frac{\text{base length}}{2}\right)^2
\]
Substituting the given values:
\[
15^2 = h^2 + 8^2
\]
Calculating the squares:
\[
225 = h^2 + 64
\]
Now, isolate \(h^2\):
\[
h^2 = 225 - 64
\]
\[
h^2 = 161
\]
Now, take the square root:
\[
h = \sqrt{161} \approx 12.6886
\]
Therefore, the height of the right pyramid is approximately \(12.69\).
That's not one of the options I gave you