Right Triangles and Trigonometry
Lesson 19
Objective
Use side and angle relationships in right and non-right triangles to solve application problems.
Common Core Standards
Core Standards
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G.SRT.D.11 — Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Criteria for Success
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- Model a contextual situation in a diagram, labeling all relevant measures and annotating the diagram with important information.
- Identify the most efficient and appropriate theorem to find the missing information in a contextual problem.
- Solve application problems efficiently and interpret the solution in the context of the problem.
- Verify solution method and justify reasoning.
Anchor Problems
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Problem 1
A surveyor needs to determine the distance between two points, $$A$$ and $$B$$, that lie on opposite banks of a river. A point $$C$$ is chosen $${160}$$ meters from point $$A$$, on the same side of the river as $$A$$. The measures of $$\angle BAC$$ and $$\angle ACB$$ are 41° and 55°, respectively. Approximate the distance from $$A$$ to $$B$$ to the nearest meter.
Guiding Questions
References
Geometry > Module 2 > Topic E > Lesson 32 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..
Problem 2
Two lighthouses are 30 miles apart on each side of the shorelines running north and south, as shown. Each lighthouse keeper spots a boat in the distance. One lighthouse keeper notes the location of the boat as 40° east of south, and the other lighthouse keeper marks the boat as 32° west of south. What is the distance from the boat to each of the lighthouses at the time it was spotted? Round your answers to the nearest mile.
Guiding Questions
References
Geometry > Module 2 > Topic E > Lesson 33 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..
Problem Set
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
- Include problems where students choose the most efficient and appropriate theorem to find the missing information in a contextual problem.
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EngageNY Mathematics Geometry > Module 2 > Topic E > Lesson 32
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Focus on the application questions
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Khan Academy Solving General Triangles
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EngageNY Mathematics Geometry > Module 2 > Topic E > Lesson 33
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Focus on the application questions
Target Task
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Your school is challenging classes to compete in a triathlon. The race begins with a swim along the shore and then continues with a bike ride for 4 miles. School officials want the race to end at the place it began, so after the 4-mile bike ride, racers must turn 30° and run 3.5 miles directly back to the starting point. What is the total length of the race? Round your answer to the nearest tenths place.
References
Geometry > Module 2 > Topic E > Lesson 33 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 Fishtank Learning, Inc.