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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  1. Model a contextual situation in a diagram, labeling all relevant measures and annotating the diagram with important information.
  2. Identify the most efficient and appropriate theorem to find the missing information in a contextual problem. 
  3. Solve application problems efficiently and interpret the solution in the context of the problem. 
  4. 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

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References

EngageNY Mathematics Geometry > Module 2 > Topic E > Lesson 32Example 1

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

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References

EngageNY Mathematics Geometry > Module 2 > Topic E > Lesson 33Example 3

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.

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