To find the height of the Great Pyramid of Giza, we can use the Pythagorean theorem. The pyramid has a square base, and we can visualize it as a right triangle formed by:
- The height of the pyramid (h).
- The slant height (l), which is the hypotenuse of the triangle.
- Half of the base length (b/2), which forms one leg of the triangle.
Given:
- The edge length (diagonal of the base) of the pyramid is \( b = 245.5 , \text{m} \).
- The slant height \( l = 190.2 , \text{m} \).
First, we need to find half of the base length:
\[ \frac{b}{2} = \frac{245.5}{2} = 122.75 , \text{m} \]
Now we can apply the Pythagorean theorem:
\[ l^2 = h^2 + \left(\frac{b}{2}\right)^2 \]
Substituting the known values:
\[ (190.2)^2 = h^2 + (122.75)^2 \]
Calculating each square:
\[ 190.2^2 = 36176.04 \] \[ 122.75^2 = 15068.0625 \]
Substituting these values into the equation:
\[ 36176.04 = h^2 + 15068.0625 \]
Now, solve for \( h^2 \):
\[ h^2 = 36176.04 - 15068.0625 \] \[ h^2 = 21107.9775 \]
Finally, take the square root to find \( h \):
\[ h = \sqrt{21107.9775} \approx 145.4 , \text{m} \]
Thus, the height of the Great Pyramid of Giza is approximately 145.4 meters.