Problem

For the square pyramid, the lateral edge length, $e$ is 25 in, and the slant height, $s$, is 24 in. Find the height of the pyramid, $h$. Round the answer to the nearest whole number. Hint Before finding the length ot $h$, you will first need to find the length of $r$ (1 point) The height of the square pyramid is $\square$ in CheckAnswer-

Solution

Step 1 :Given that the lateral edge length, $e$ is 25 in, and the slant height, $s$, is 24 in.

Step 2 :We need to find the height of the pyramid, $h$. But before finding $h$, we first need to find the length of $r$.

Step 3 :We can find $r$ using the Pythagorean theorem, since the lateral edge, $e$, the half of the base edge, $r$, and the slant height, $s$, form a right triangle. So, $r = \sqrt{e^2 - s^2}$.

Step 4 :Substituting the given values, $r = \sqrt{25^2 - 24^2} = 7$ in.

Step 5 :Now, we can find the height, $h$, using the Pythagorean theorem. The slant height, $s$, the half of the base edge, $r$, and the height, $h$, form a right triangle. So, $h = \sqrt{s^2 - r^2}$.

Step 6 :Substituting the values, $h = \sqrt{24^2 - 7^2} = 23$ in.

Step 7 :Final Answer: The height of the square pyramid is \(\boxed{23}\) in.

From Solvely APP
Source: https://solvelyapp.com/problems/FymfYzlGsB/

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