Finding Angle Measurements Using Trig

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Objective

Students will be able to find angle measures using trigonometry, and apply their knowledge to solving triangles. Students also derive the Law of Sines.

Big Idea

Students put their knowledge of trig to work solving problems and proving hypotheses involving angles.

Lesson Author

Beth Menzie

Amsterdam, NY

Grade Level

Tenth grade

Subjects

Math

law of sines

Trigonometry

trigonometric ratios

Geometry

Standards

HSG-SRT.C.6

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

HSG-SRT.C.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*

HSG-SRT.D.10

(+) Prove the Laws of Sines and Cosines and use them to solve problems.

Introductory Problem

3 minutes

As the students enter the room, the Lighthouse Problem is on the board and I hand out a paper copy to the students. I ask the students to set up the problem. They are familiar with angle of elevation and depression, but their work may come to a screeching halt when it comes to actually finding the angle. After giving students a minute or two to think about it, I plan to introduce the inverse trig functions on the graphing calculator, and then allow them to finish this problem, as well as the other problems included at the end of the lighthouse problem. This type of opening often motivates my students to pay attention for the rest of the lesson. Caution: New Skills Ahead!

Solving More Problems

40 minutes

About these problems

To begin this segment of the lesson I hand out the Finding Angle Measures problem set. It includes 3 types of problems:

Standard problems in which the students use trigonometry to find angles and lengths of sides of right triangles, including 2 word problems in which students must draw their own diagrams. (Problems 1-8)
Non-standard problems in which the students are given figures without right angles. The students will need to draw in the heights of the figures in order to solve the problems using trig. (Problems 9 and 10)
Problems in which the students focus on the definitions of the trig functions to answer the questions. These problems include proving the Pythagorean identities and the Law of Sines. For those students needing scaffolding, I have included a modified version of this assignment, which helps to lead them through the steps of the proofs. (Problems 11-13)

I also provide Answers to Finding Angle Measures that can be handed out to the students or posted somewhere in the room, so that they can check their work periodically. Students work in their groups, and I walk around the room providing support questions where needed.