I was looking through this online material. It gives a motivational algebra problem about a flagpole at the very beginning in the prolog. How was the equation obtained? I tried to set it up and ended up with a messy fourth order equation.

Here is the approach I took. Label as y the distance in the After picture from the end of the building on the ground to the top of the flagpole. From triangle similarity, we get x/10 = 10/y, giving y = 100/x. Then I used the Pythagorean equation for the large triangle: (10+x)^^2 + (10+y)^^2 = (100 – x)^^2. I plugged in the value for y, multiplying everything by x^^2 to clear the denominator to get a fourth order equation that looked nothing like the equation in the book.

I plugged in the values given for x given in the book and the values were pretty close.