The document provides examples and explanations of using indirect measurement to find unknown heights or lengths. It gives two examples of setting up proportions using corresponding sides of similar triangles to calculate heights that cannot be measured directly. The examples find the height of a tree using a 6 foot person and 7 foot shadow, and the height of a rocket using a 4 foot model rocket and its 3 foot shadow. It explains that indirect measurement, also called using similar figures and proportions, allows calculating heights by setting up and solving proportions.

1. Warm Up Lesson Presentation Problem of the Day 7-5 Indirect Measurement Course 1

2. Warm Up Find the missing value in each proportion. 1. = 2. = 3. = 4. = t = 15 k = 5 n = 56 x = 84 6 t __ 18 45 __ k 19 __ 20 76 __ 6 8 __ 42 n __ 21 11 __ x 44 __

3. Problem of the Day Bryce, Kate, and Annie have drawn rectangles. Each side of Bryce’s rectangle is twice the size of one side of Kate’s. The same side of Kate’s rectangle is congruent to one side of Annie’s. One side of Annie’s rectangle is congruent to one side of Bryce’s. Which two rectangles could be congruent? Kate’s and Annie’s

4. Learn to use proportions and similar figures to find unknown measures .

5. Vocabulary indirect measurement

6. One way to find a height that you cannot measure directly is to use similar figures and proportions. This method is called indirect measurement .

7. Additional Example 1: Using Indirect Measurement Use the similar triangles to find the height of the tree. = h • 2 = 6 • 7 2 h = 42 = h = 21 Write a proportion using corresponding sides. The cross products are equal. h is multiplied by 2. Divide both sides by 2 to undo multiplication. The tree is 21 feet tall. 2 7 __ 6 h __ 2 h 2 ___ 42 2 ___

8. Check It Out: Example 1 Use the similar triangles to find the height of the tree. = h • 3 = 6 • 9 3 h = 54 = h = 18 Write a proportion using corresponding sides. The cross products are equal. h is multiplied by 3. Divide both sides by 3 to undo multiplication. The tree is 18 feet tall. 3 ft. 9 ft. 6 ft. h 3 9 __ 6 h __ 3 h 3 ___ 54 3 ___

9. Additional Example 2: Measurement Application A rocket casts a shadow that is 91.5 feet long. A 4-foot model rocket casts a shadow that is 3 feet long. How tall is the rocket? = 4 • 91.5 = h • 3 366 = 3 h = 122 = h Write a proportion using corresponding sides. The cross products are equal. h is multiplied by 3. Divide both sides by 3 to undo multiplication. The rocket is 122 feet tall. 91.5 3 ____ h 4 __ 366 3 ___ 3 h 3 ___

10. Check It Out: Example 2 A building casts a shadow that is 72.5 feet long when a 4-foot model building casts a shadow that is 2 feet long. How tall is the building? = 4 • 72.5 = h • 2 290 = 2 h = 145 = h Write a proportion using corresponding sides. The cross products are equal. h is multiplied by 2. Divide both sides by 2 to undo multiplication. The building is 145 feet tall. 72.5 2 ____ h 4 __ 290 2 ___ 2 h 2 ___ h 72.5 ft 2 ft 4 ft

11. Lesson Quiz 1. Use the similar triangles to find the height of the post. 2. On a sunny afternoon, a goalpost casts a 75 ft shadow. A 6.5 ft football player next to the goal post has a shadow 19.5 ft long. How tall is the goalpost? 25 feet 20 feet 8 ft 6 ft x 15 ft