5-10 Indirect Measurement
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1 1. A basketball hoop in Miguel s backyard casts a shadow that is 8 feet long. At the same time, Miguel casts a shadow that is 4.5 feet long. If Miguel is 5.5 feet tall, how tall is the basketball hoop? Round to the nearest tenth. 5. The triangles below are similar. Find x. 9.8 ft 2. In the figure,. Find the distance across Stallion Ravine. 120 yd 6. The triangles below are similar. How far is it from Athens to Yukon? 198 m 3. A flagpole is 30 feet high, and a mailbox is 3.5 feet high. The mailbox casts a shadow that is 5.25 feet long. How long is the flagpole s shadow at the same time? 45 feet 4. The height of Medina Middle School is 25 feet tall. A mail service drop box outside the school is 4 feet tall. The drop box casts a shadow that is 6 feet long. At the same time, what is the length of the shadow of the school building? 37.5 ft 40 mi 7. The height of a roller coaster is feet. If the roller coaster s shadow is 60 feet long, how long will a person s shadow be if the person is 5 feet 3 inches tall? 2 ft esolutions Manual - Powered by Cognero Page 1
2 8. All of the triangles in the figure below are similar. 10. Electrical poles that carry electrical wire seem to get smaller the farther away they are. Find the apparent height of each pole if the tallest pole is 50 feet tall, and the distance between each pole is 100 feet. a. Find the measure of segment GD. b. If segment GF is congruent to segment FE, find the measure of segment BF. c. If the length of segment AD is 15 meters, what are the lengths of segments BC and CD? a. 12 m b m c. CD = 7.5 m, BC = Multiple Representations In this problem, you will investigate similar triangles. Consider the following situation. A biplane starts to take-off from the beginning of a runway. When the plane is level with the end of the runway, it is 500 feet above the ground. A bird is flying in the same direction. It is 8 feet above the ground and 15 feet from the beginning of the runway. a. Model Draw a diagram of the situation. b. Symbols Write and solve a proportion to find how far the plane is from the beginning of the runway. a. 1st pole = 50 ft, 2nd pole = 37.5 ft, 3rd pole = 25 ft, 4th pole = 12.5 ft 11. During a basketball game, Josh, Devon, and Marco are in the following positions. Josh is 16 feet from Devon, and Devon is 5 feet from Marco. If Marco is 4 feet from both A and B, how wide is the key? 12 ft b. ; ft esolutions Manual - Powered by Cognero Page 2
3 12. Use the figure below. a. Write two different proportions that could be used to determine the height of the lighthouse. b. How tall is the lighthouse? 16. Persevere with Problems In the diagram below,. a. Write a proportion that could be used to solve for the height h of the flag pole. b. What information would you need to know in order to solve this proportion? a. ; b. 200 ft 13. The Navy Pier Ferris Wheel in Chicago is 150-feet tall. If the Ferris wheel casts a 37 -foot shadow, write and solve a proportion to find the height of a woman standing nearby who casts a 1 shadow. ; 6 ft -foot 14. A tree house casts a shadow of 18 feet while Jenet casts a shadow 9 feet. If Jenet is 5 feet tall, how tall is the tree house? 10 ft 15. Model with Mathematics Write a real-world problem to describe how you could determine the height of a local landmark or statue in your community using shadow reckoning. See students work. a. b. The distance from the mirror to the person, the distance from the mirror to the base of the flag, the height of the person. 17. Justify Conclusions True or false? If two pairs of corresponding sides of two triangles are proportional, then you can use indirect measurement to determine the length of a missing side. Explain your reasoning. false; Sample answer: You also need to know if the angles are congruent. 18. Building on the Essential Question Give a realworld example of when you might need to use indirect measurement. Explain how you would solve the problem. Sample answer: You can use indirect measurement to find the height of a tree in order to hang a swing from the tree. You can set up a proportion comparing your height to the height of the tree and the length of your shadow to the length of the tree s shadow. esolutions Manual - Powered by Cognero Page 3
4 19. A bell tower casts a 60-inch shadow. At the same time, a statue that is 4.5 feet tall casts a 15-inch shadow. How tall is the bell tower? 21. SHORT RESPONSE Find the length in kilometers of Beechwold Boulevard. A 200 ft B 30 ft C 27 ft D 18 ft 10 km 22. How tall is the street sign? D 20. In the figure, PRT ~ SRQ. Find the distance across the golf green. A 3.15 m B 3.5 m C 3.75 m D 3.8 m A F 4.5 ft G 35 ft H 48 ft J 72 ft 23. Triangle JMK is similar to triangle PRO. What is the value of x? J 13.5 esolutions Manual - Powered by Cognero Page 4
5 24. How many 6-inch long pieces of ribbon can be cut from a piece that is 3 yards long? pieces Write each fraction as a decimal x Find each square root. 9 5 no real solution ±7 0.6 Evaluate each expression if x = 2, y = 3, and z = z (xz) xy 2 esolutions Manual - Powered by Cognero Page 5
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A circle is the set of points that are equidistant from a special point in the called the.
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