To find the height of the square pyramid, we can use the Pythagorean theorem in the context of the pyramid's geometry.
Assuming you have a square pyramid where the base is a square and you know the slant height and half of the side length of the base, we can find the height.
Given:
- Slant height = 84 in.
- Base edge = 58 in.
- Half of the base edge = 58 in / 2 = 29 in.
The height \( h \), slant height \( l \), and half the base edge \( a \) form a right triangle:
\[ l^2 = h^2 + a^2 \]
Substituting the known values:
\[ 84^2 = h^2 + 29^2 \]
Calculating: \[ 84^2 = 7056 \] \[ 29^2 = 841 \]
Now plug these values into the equation:
\[ 7056 = h^2 + 841 \]
Subtract 841 from both sides:
\[ 7056 - 841 = h^2 \] \[ 6215 = h^2 \]
Now take the square root of both sides to solve for \( h \):
\[ h = \sqrt{6215} \approx 78.8 \text{ in} \]
So the height of the square pyramid is approximately:
\[ \text{Height} \approx 78.8 \text{ in} \]
In your response box, you would enter:
78.8 in.