To find the length of the edge of the square base of the pyramid, we can use the Pythagorean theorem. We know the height of the pyramid (h) is 321 ft, and the slant height (l) is 436.5 ft. In a right triangle formed by half of the base length (b/2), the height, and the slant height, we can set up the equation:
\[ l^2 = h^2 + \left(\frac{b}{2}\right)^2 \]
Substituting the known values:
\[ (436.5)^2 = (321)^2 + \left(\frac{b}{2}\right)^2 \]
Calculating \( (436.5)^2 \) and \( (321)^2 \):
\[ 436.5^2 = 190,616.25 \] \[ 321^2 = 103,680 \]
Now plugging these values into the equation:
\[ 190,616.25 = 103,680 + \left(\frac{b}{2}\right)^2 \]
Now, subtract \( 103,680 \) from both sides:
\[ 190,616.25 - 103,680 = \left(\frac{b}{2}\right)^2 \]
Calculating the left side:
\[ 86,936.25 = \left(\frac{b}{2}\right)^2 \]
Now, take the square root of both sides to find \( \frac{b}{2} \):
\[ \frac{b}{2} = \sqrt{86,936.25} \approx 294.8 \]
Now, multiply by 2 to find \( b \):
\[ b \approx 2 \times 294.8 \approx 589.6 \]
Thus, the length of the edge of the square base rounded to the nearest tenth is:
\[ \boxed{589.6} \text{ ft.} \]
15 answers