Right Triangles and Trigonometry

Lesson 13

Objective

Solve a modeling problem using trigonometry.

Common Core Standards

Core Standards

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  • G.SRT.C.8 — Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Criteria for Success

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  1. Identify the variables that need to be considered with a real-life modeling problem. 
  2. Identify necessary information to solve the problem. 
  3. Model a problem with trigonometric ratios. 
  4. Adjust a model based on the reasonability of solutions.

Tips for Teachers

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  • This is the second lesson out of two that has the students model real-world examples of trigonometric ratios. 
  • The following resource may be helpful to fully understand the Anchor Problems: Dy/dan, Dan Meyer, “[Makeover] Marine Ramp”.

Anchor Problems

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Problem 1

Watch the video "Marine Ramp" by Dan Meyer and determine which bridge is best.

Guiding Questions

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References

101Questions Marine Ramp

Marine Ramp by Dan Meyer is made available on 101Questions under the CC BY 3.0 license. Accessed Feb. 28, 2018, 3:38 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Write a model that describes how to find the optimal ramp length, regardless of the horizontal and vertical displacement of the pier and the ramp. 

Use the following link, Boat Dock, to test out your model in different scenarios.

Guiding Questions

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References

101Questions Marine RampSequel, "Boat Dock"

Marine Ramp by Dan Meyer is made available on 101Questions under the CC BY 3.0 license. Accessed Feb. 28, 2018, 3:38 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 information is presented verbally and students need to draw a diagram to find the solution.

Target Task

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What is the optimal length for a ramp that has a horizontal displacement of 26 meters from the pier and a vertical displacement of 9.5 meters from the pier? 

Use your model from Anchor Problem #2 to find this value and justify your reasoning using a diagram and explanation.