Chapter 8.2, Problem 53AYU

To determine

To find: The current height of the Great Pyramid.

Answer to Problem 53AYU

The current height of the Great Pyramidis $450.56\text{ft}$ .

Explanation of Solution

Given information:

The given figure is,

  

Consider the following figure,

  

From the figure, calculate thebase,

  $\begin{array}{l}\tan \left(40.3°\right)=\frac{h}{x+200}\\ x=\frac{h}{\tan 40.3°}-200\\ x=1.179h-200\end{array}$

The current height of the Great Pyramidis calculated as,

  $\begin{array}{l}\text{tan46}\text{.27}°=\frac{h}{x+100}\\ \text{tan46}\text{.27}°=\frac{h}{\left(1.179h-200\right)+100}\\ 1.232h-104.53=h\\ h=450.56\text{ft}\end{array}$

Therefore, the current height of the Great Pyramid is $450.56\text{ft}$ .