Superlesson
Project 7-4
Algebra
Chapter 7, Lines and Distance
Television and the news play a large part in all of our lives. In this section we will explore proportional reasoning though the use of fire trucks...something we see in the news too often!
Part A, Similar Figures and Proportions
1. Open the Fire trucks Web site.
a. Assume that the ladder shown on the truck is 40 feet long from the edge of the platform to the base of the truck. Using proportional reasoning, how long is the fire truck?
b. Using the same proportions, how high from the ground is the hood of the truck?
c. Construct a drawing of the fire truck that is five times the size of the one on your computer screen. You may want to use a grid and enlarge the truck in small sections. Explain why your drawing is similar to the one on your computer screen.
Part C, Right Triangle Trigonometry
2. Continue examining the Fire trucks site.
a. Browse through this site to find the range of degrees for the ladder adjustment.
b. If the ladder is fully extended to 95 feet, how far away from the building will the base of the ladder be if it reaches a point on the side of the building 30 feet from the ground?
3. What angle would the ladder make with the truck if extended as in 2b?
Part D, Making Connections
4. Continue using the fire truck site. Suppose that firemen are using a 75- foot ladder extended to 70 feet. They encounter a fire, but since the wind is blowing, they are reluctant to increase the angle of the ladder with the truck beyond 60 degrees. How many vertical feet will the ladder extend from the top of the fire truck?
5. If the firemen extend the 70-foot ladder at a 45 degree angle, how many vertical feet will the ladder extend from the top of the fire truck? Find your answer in two different ways.