To find the height of the Great Pyramid of Giza, we can use the Pythagorean theorem. The pyramid has a square base, and the height, half the edge length of the base, and the slant height form a right triangle.
Let's denote:
- \(h\) as the height of the pyramid,
- \(s\) as the slant height (180.2 m),
- \(a\) as half the edge length of the base.
First, we'll calculate \(a\): \[ a = \frac{230.5 , \text{m}}{2} = 115.25 , \text{m} \]
Now, we set up the Pythagorean theorem: \[ s^2 = h^2 + a^2 \]
Substituting in the values: \[ (180.2)^2 = h^2 + (115.25)^2 \]
Calculating the squares: \[ 180.2^2 = 32472.04 \] \[ 115.25^2 = 13272.5625 \]
Now substitute back into the Pythagorean theorem: \[ 32472.04 = h^2 + 13272.5625 \]
To isolate \(h^2\), subtract \(13272.5625\) from both sides: \[ h^2 = 32472.04 - 13272.5625 \] \[ h^2 = 19199.4775 \]
Taking the square root to find \(h\): \[ h = \sqrt{19199.4775} \approx 138.634 \]
Rounding to the nearest tenth, the height of the pyramid is: \[ \boxed{138.6} , \text{m} \]
2 answers