Use properties of similar triangles to model and solve real-world problems.
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You want to determine the approximate height of one of the buildings in the city. You are told that if you place a mirror some distance from yourself so that you can see the top of the building in the mirror, then you can indirectly measure the height using similar triangles. Let point $$O$$ be the location of the mirror so that the person shown can see the top of the building.
If you know that the distance from eye-level straight down to the ground is 5.3 feet, the distance from the person to the mirror is 7.2 feet, and the distance from the mirror to the base of the building is 1,742.8 feet, then what is the height of the building?
Grade 8 Mathematics > Module 3 > Topic B > Lesson 12 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Modified by The Match Foundation, Inc.A geologist wants to determine the distance across the widest part of a nearby lake. The geologist marked off specific points around the lake so that the line containing $${\overline{{DE}}}$$ would be parallel to the line containing $${\overline{{BC}}}$$. The segment $${BC}$$ is selected specifcally because it is the widest part of the lake. The segment $${DE}$$ is selected specifically because it is a short enough distance to easily measure.
The geologist has made the following measurements: $$\left | {DE} \right |$$=5 feet, $${\left | AE \right |}$$= 7 feet, and $${\left | EC \right |}$$ = 15 feet. Can she determine the length across the widest part of the lake?
Grade 8 Mathematics > Module 3 > Topic B > Lesson 12 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Modified by The Match Foundation, Inc.?
The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Henry thinks he can figure out how high his kite is while flying it in the park. First, he lets out 150 feet of string and ties the string to a rock on the ground. Then he moves from the rock until the string touches the top of his head. He stands up straight, forming a right angle with the ground. He wants to find out the distance from the ground to his kite. He draws the following diagram to illustrate what he has done.
Grade 8 Mathematics > Module 3 > Topic B > Lesson 12 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Modified by The Match Foundation, Inc.?