Is the triangle a right triangle? Who is Pythagoras? CPM Materials modified by Mr. Deyo. IM 8 Ch How Can I Find Lengths In Three Dimensions
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1 Common Core Standard: 8.G.7 Is the triangle a right triangle? Who is Pythagoras? CPM Materials modified by Mr. Deyo
2 Title: IM8 Ch How Can I Find The Lengths in 3 Dimensions? Date: Learning Target By the end of the period, I will apply the Pythagorean Theorem to problems in a variety of two dimensional, real world contexts. I will demonstrate this by completing Four Square notes and by solving problems in a pair/group activity.
3 Home Work: Sec Desc. Date Due Review & Preview 4 Problems 9 139, 9 140, 9 141, 9 142
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5 Vocabulary 1) right triangle 2) leg(s) (a & b) 3) hypotenuse (c) 4) Pythagorean Theorem a 2 + b 2 = c 2
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7 9.2.6 How Can I Find The Lengths in Three Dimensions? You have been studying right triangles from a two dimensional viewpoint. However, often triangles occur in three dimensional settings. In this lesson, you will build a model, use it to visualize the location of right triangles in a three dimensional situation, and then make calculations to find the triangle lengths The roof on the Flat Family s house is one large flat rectangle. It is parallel to the ground. The TV antenna is mounted in the center of the roof. Guy wires are attached to the antenna five feet below its highest point, and they are attached to the roof at each corner and at the midpoint of each edge. These wires support the antenna in the wind. Each guy wire is the hypotenuse of a right triangle. Mr. Flat needs to know how long each wire needs to be to keep the antenna upright. He also needs to find the total amount of wire needed. a) Build a model of the Flat Family Roof. The model will serve as a reference while your team finds the lengths of the sides of the right triangles in a three dimensional setting.
8 135 a) Build a model of the Flat Family Roof. The model will serve as a reference while your team finds the lengths of the sides of the right triangles in a threedimensional setting. 1) For the roof, use a rectangular piece of cardboard. Draw the diagonals of the rectangle to locate the center. 2) Tape the string guy wires to the antenna (straw). Do not forget to leave a gap that represents the five feet between the strings and the top of the antenna. How many guy wires are there? 3) Attach the antenna to the center of the roof. Use tape, tie knots, or make slits to anchor your antenna and guy wires to the roof. Top View Front View
9 9 135 b) Locate as many vertical right triangles as you can on your model. How many right triangles did you find? c) Identify which right triangles are the same size and which are different sizes. How many different sized right triangles did you find? How many of each size are there? d) Sketch each of the different sized right triangles on a different color of paper. Cut out the triangle. Tape the triangle in position on your model.
10 9 136a) The Flat Family s roof is 60 feet long and 32 feet wide. The TV antenna is 30 feet tall. The wires are attached five feet below the top of the antenna. a) How long must each guy wire be? Show all of your steps to get your solution.
11 9 136b) The Flat Family s roof is 60 feet long and 32 feet wide. The TV antenna is 30 feet tall. The wires are attached five feet below the top of the antenna. b) Mr. Flat needs to buy the wire at his local hardware store. He decides to buy an additional 10% more than the amount that you calculated so that he can attach the wires on each end. How much total wire should he buy? Show all of your work so that Mr. Flat can understand it, and round your answer reasonably.
12 A child s shoe box measures 4" by 6" by 3". What is the longest pencil you could fit into this box? An empty box may help you visualize the various ways you could fit the pencil in the box. If possible, draw a diagram to show the pencil s position. Show your steps. Explore using 3D Model Box (CPM). Click and drag the box to rotate. The longest pencil that fits in the box is inches long.
13 Additional Challenge: A fly was sitting on the ground in the back left corner of your classroom. He flew to the ceiling in the opposite corner of the room. How far did he fly if he went in a straight line? Draw a diagram of your classroom, complete with the correct measurements. Write equations. Show your steps. Draw a diagram and label it. Write equations and find the missing length. Is the length irrational?
14 The hypotenuse and one leg of a right triangle are 65 and 60 meters. What is the length of the third side? chapter/c 65m 60m The length of the third side is meters.
15 Find the missing length on this right triangle. The length of the missing side is millimeters.
16 9 141a,b. Solve these equations for x. a) b) (x + 3.5)2 = x = x
17 9 141c,d. Solve these equations for x. c) d*) 3x = (6.6 + x) 5x = x
18 9 142a,b. Simplify each of the following expressions. chapter/c a) b) x( 2) 10x
19 9 142c,d. Simplify each of the following expressions. chapter/ch9/le. 4 2 c) 1 d) 4 ( ) xy 3 ( ) 3 xy 3
20 Complete the table. homework/homework/category/cc/textbook/cc3/ chapter/ch9/lesson/9.2.6/problem/9 143 Put the (x,y) coordinate pairs in numerical order from least to greatest. x y a) Find the rule. y = mx + b b) What is the slope? y = ( )x + ( )
21 Additional Challenge: Use the diagram and your answer to problem above. If your classroom measured 30 ft by 30 ft by 10 ft, what distance would the fly travel? chapter/ch9/lesson/9
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