Question

The great pyramid of Giza in Egypt has a square base with edge length of 230.5 m and a slant height of 180.2 m. Find the height of the pyramid. Round to the nearest tenth

Answer 1

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:
\[
\boxed{138.6} \, \text{m}
\]