Applications to Pythagorean Theorem
Course: Algebra ˝
I. Review homework (10 min)
II. Anticipatory Set (5 min)
How many of you have ever climbed a ladder up to a roof or a high place? What was the ladder leaning against? What shape is formed by the ladder, the object it’s leaning against, and the ground?” (A right triangle). Draw. Today we are going to use the Pythagorean theorem that we learned yesterday to find out the lengths of the sides of the triangle. What is the Pythagorean theorem? (a2+b2=c2). C represents what part of the right triangle?
III. Problem (10 min).
I am short and want to be able to reach the top of the chalkboard. I am going to place a ladder against the board so that it leans against the wall and stops at the top of the chalkboard. If the ladder is 8 feet long, how far away from the wall does the ladder need to be?
A. Have students draw the picture and label
B. ASK: What information do you know? What information do you need to know? How can we find that information? Have a few students come up and measure to the top of the chalkboard. Which of these objects represents the hypotenuse? Work in pairs to discuss how you might find the answer to the problem.
C. Walk around the room and make sure that students are working and see if they have questions.
D. Have students share answers and how they found them. Have a student show the answer on the board.
IV. Practice (15 min)
In your pairs, each group will have to find:
1) the diagonal of the desk, by only measuring the sides,
2) The distance of the door to the wall, when the door is ˝ way opened, and
3) The distance of a plane from the point of take off, if the plane has traveled 3,500 feet and is 2,600 feet from the ground.
All work must be shown and each student must turn in their own paper containing a diagram, dimensions, and all work.
Discuss the strategies used to solve the problems. What did the students do? How did they measure? Why isn’t everyone’s answer for number 2 going to be the same? What were some difficulties that they had?
VI. Close (5 min)
Journal: what is the importance of the Pythagorean theorem and when could it be useful?