Q29. - Algebra 2

Question

Mayan Indians of Mexico and Central America built pyramids that were used as their temples. Ancient Egyptians built pyramids to use as tombs for the pharohs. Estimate the slope that a face of each pyramid makes with its base.

The Pyramid of the Sun in Teotihuacan, Mexico, measures about $700$ feet on each side of its square base and is about $210$ feet high.

Step-by-Step Solution

Answer

The slope of the Pyramid is $-\frac{3}{5}$

Step-1- How to find the slope of a line.

The slope m of a line passing through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by

$m=\frac{y_2-y_1}{x_2-x_1}$, where $x_2\ne x_1$

Step-2 – Summarizing the conditions

Given that the base of pyramid is about 700 feet on each side of its square base is about 210 feet high.

We generalized, the pyramid in $2D$ as triangle with base $\frac{700}{2}=350$ feet and $210$ feet.
 In co-ordinates form, we write the co-ordinates of  $▵OAB$ as

$O\left(0,0\right),A\left(350,0\right),B\left(0,210\right)$

Step 3 - Finding the Slope

Slop of pyramid is obtained from the line $AB$

So, 

$\begin{array}{c}m=\frac{210-0}{0-350}\\ =-\frac{210}{350}\\ =-\frac{3}{5}\end{array}$