### Millennium Hotel St. Louis Cabana Math Projects

P2 (-183.1437, 176.8096)           P10 (-183.1437, 42.25752)           P23 (-243.6437, 42.25752)
P34 (-251.1437, 42.25752)           P33 (-236.1437, 42.25752)           P31 (-213.1437, 42.25752)
P32 (-153.1437, 42.25752)           P22 (-276.1524, -23.1719)           P21 (-90.13497, -23.1719)
P20 (-283.3214, -38.58633)           P19 (-82.96593, -38.58633)           P18 (-290.4905, -54.00077)
P17 (-75.79688, -54.00077)

The Millennium Hotel St. Louis has two "Cabana" wings sweeping out from the North Tower. Looking down on the hotel design makes these wings look like blades of a propeller. However, a hotel guest would not see the North Cabana when looking down from a North Tower room since the blade is covered by a bank.

Your mission is to write the equations of the arcs of the North Cabana. P2 is the center of the arc between P21 and P22 as well as the arc between P17 and P18. Do not forget to limit the x and y values in such a way that you select just that part of the circle that you want for the arc.

Write the equation of the line from P21 to P17 and the equation of the line from P22 to P18. Again, don't forget to limit x values to select the line segment from one point to the other.

The South Cabana is visible from southern rooms in the North Tower or from northern rooms in the South Tower. P40 is the center of the corresponding two arcs for this cabana. You will find coordinates for points on the South Cabana blade in other parts of Millennium Hotel St. Louis project. When you complete the South Cabana, North Tower and South Tower equations you will have a border around all the guest rooms of the hotel. How would you change there border equalities to represent the region inside the borders? Can you find the area covered by the region within the borders?

With thanks to the following college algebra students: Lawrence Fournier Jr., Jeremy Freeman, Joseph Koepke, Philip O'Brian, Nathan Remer and Joshua Tadrick on their Regal Riverfront Hotel graphs and calculations.

A "Service Learning" Project to provide web pages for our community's better understanding of mathematics.

Danielle, Darlene, Kellie, Jill, Nanyal, Kevin, Rachel, Christina, Jennifer, Candice, Vance, Esther and Melinda demonstrate calculations using distance formulas and equations of circles.

Millennium Hotel St. Louis Math Projects