Right Triangles and Trigonometry
Lesson 11
Objective
Find the angle measure given two sides using inverse trigonometric functions.
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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- Identify sine, cosine, and tangent as trigonometric functions as well as relationships between side lengths in right triangles.
- Describe that because they are functions, we need to be able to UNDO them (just like addition, subtraction, etc.).
- Calculate the inverse of sine, cosine, and tangent using technology—called arcsine, arccosine, and arctangent. They are also noted as $${\mathrm{sin}^{-1}(x)}$$, $${\mathrm{cos}^{-1}(x)}$$, and $${\mathrm{tan}^{-1}(x)}$$ respectively.
- Use the understanding that when you give the arcsine of a value, you are saying, “What angle gives me a sine of ______?” to solve problems.
- Use the inverse trigonometric functions to find the angle measures from the given ratios.
Tips for Teachers
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- This lesson is an extension of G-SRT.8, which does not specifically mention using inverse trigonometric function. This lesson will prepare students to access F.BF.4 standard in Algebra II.
- Anchor Problem #1 will require the teacher to do a significant amount of modeling to define the inverse of sine, cosine, and tangent as arcsine, arccosine, and arctangent, respectively.
Anchor Problems
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Problem 1
Find the value of the side length marked $$x$$.
Guiding Questions
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Problem 2
Given the following right triangle, find all of the angle measures to the nearest degree.
Guiding Questions
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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 are given a real-life scenario and they must find the missing angles and side-length measures.
- Include problems where students need to identify at least two ways of solving a problem—either using the Pythagorean theorem, trigonometric ratios, or inverse trigonometric ratios.
- Include error analysis where the error is using the incorrect trigonometric ratio to find a missing value.
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Mathematics Vision Project: Secondary Mathematics Two Module 6: Similarity and Right Triangle Trigonometry
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Lessons 10 and 11 (Do not use any questions pertaining to angle of elevation or depression, which will be used in Lesson 12)
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EngageNY Mathematics Geometry > Module 2 > Topic E > Lesson 34
Target Task
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Find the measure of $${\angle CAB}$$. Round angle measures to the nearest degree. Use two different trigonometric ratios.
