FINDING THE HEIGHT OF A PYRAMID The Great Pyramid of Cheops in Egypt has a squar...

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October 2022 1 2 Report

FINDING THE HEIGHT OF A PYRAMID The Great Pyramid of Cheops in Egypt has a square base with side length of 800 feet. Its triangular faces are almost equilateral.

a. Explain how to find the height of each triangle in the diagram at the right. What is the height of each triangle? Write the height as a simplified radical.

b. Explain how to find the height of the pyramid. What is the height of the pyramid? Write the height as a simplified radical.

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$\begin{gathered}\begin{array}{l}{A. \: \rm In \: the \: △ABC, Using \: Pythagorean \: Theorem} \\ \sf h = \sqrt{800^{2} - 400^{2}} \\ \sf h = \sqrt{480000} \\ \sf h = 400\sqrt{3} \\ \\ \rm Answer: \small \boxed{\sf The \: height \: of \: each \: triangle \: is \: 400\sqrt{3} \: ft} \\ \ \ \\ {B. \: \sf The \: solid \: figure \: shown \: to \: the \: attached \: picture} \\ \textrm{To find the point G is the center of square base.} \\ \\ So, \\ {{\rm{ FG = \frac{1}{2}AD}}}\Longrightarrow {\bold {\boxed {\frac{1}{2} × 800}}} \Longrightarrow {\bold {\boxed{400}}} \\ \\ \sf{According \: to \: A, we \: can \: know \: EF = 400\sqrt{3}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{In \: △FGE}, \\ GE = \sqrt{EF^{2} - FG^{2}} \\ GE = \sqrt{(400\sqrt{3})^{2} - 400^{2}} \\ GE = \sqrt{320000} \\ GE = 400\sqrt{2} \\ \\ \rm Answer: \small \boxed{\sf The \: height \: of \: the \: pyramid \: is \: 400\sqrt{2} \: ft}\end{array} \end{gathered}$

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