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 the answer to the nearest tenth.(1 point)
Responses

138.5 m
138.5 m

175.6 m
175.6 m

150.3 m
150.3 m

160.8 m

Answer 1

To find the height of the Great Pyramid of Giza, we can use the Pythagorean theorem. The height (h), half of the base length (b/2), and the slant height (l) form a right triangle.

1. The base edge length is given as 230.5 m, so half of the base length is:
\[
\frac{b}{2} = \frac{230.5}{2} = 115.25 \text{ m}
\]

2. The slant height (l) is provided as 180.2 m.

3. We can now apply the Pythagorean theorem:
\[
l^2 = h^2 + \left(\frac{b}{2}\right)^2
\]
Substituting the known values:
\[
180.2^2 = h^2 + 115.25^2
\]

4. This computes to:
\[
180.2^2 = 32472.04
\]
\[
115.25^2 = 13273.5625
\]

5. Now plug these values into the equation:
\[
32472.04 = h^2 + 13273.5625
\]

6. Rearranging the equation to solve for \(h^2\):
\[
h^2 = 32472.04 - 13273.5625
\]
\[
h^2 = 19198.4775
\]

7. Taking the square root to find \(h\):
\[
h = \sqrt{19198.4775} \approx 138.5
\]

So, rounding to the nearest tenth, the height of the pyramid is approximately **138.5 m**.