About This Chapter
Triangle Trigonometry - Chapter Summary
Early mathematicians studied the relationships among the angles and the sides of triangles, and by doing so developed the laws and theorems of trigonometry that we use for solving advanced equations. These lessons about triangle trigonometry give you a deeper understanding of the most essential theorems, formulas, and concepts needed for solving sample trigonometric equations.
While this chapter does address a significant amount of information, our instructors have found ways to make everything easier to understand. For starters, each chapter has been split into miniaturized lessons, so instead of scrolling through a seemingly endless chapter, you can pick the individual lesson topics you want to go over. We also keep each lesson brief, making sure you remain focused on the most essential information. By completing this chapter, you will be able to do the following:
- Describe trigonometric similarity and ratios
- Identify how to find trigonometric ratios
- Analyze the cosine and sine of complementary angles
- Point out steps for solving right triangle sample problems
- Review the use and applications of the Pythagorean Theorem
- Show how to use the Pythagorean Theorem for finding distances
- Determine how the Pythagorean Theorem applies to trigonometry
- Establish finding the area of a triangle using sine
- Apply the law of cosines and the law of sines to practice problems
1. Trigonometric Ratios and Similarity
Where do terms like sine, cosine and tangent come from? In this lesson, we'll learn about how similarity with right triangles leads to trigonometric ratios.
2. Practice Finding the Trigonometric Ratios
So you know what sine, cosine and tangent are. Great! But how do you use them? Find out how in this lesson as we find missing sides and angles using trigonometric ratios.
3. The Pythagorean Theorem: Practice and Application
The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.
4. Calculating Angles for a 5-12-13 Triangle
How do you calculate the angles of a triangle when you only know the lengths of the sides? This lesson will go over a step-by-step process to calculate the angles, using a triangle whose sides are 5, 12 and 13 units long.
5. Finding Distance with the Pythagorean Theorem
How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.
6. Trigonometry and the Pythagorean Theorem
Explore how the Pythagorean Theorem can be used in conjunction with trigonometric functions. In this lesson, take an inverse trigonometric function, and define all three sides of a right triangle.
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Other chapters within the Trigonometry: High School course
- Real Numbers: Types and Properties
- Absolute Value Equations
- Working with Complex Numbers
- Coordinate Geometry Review
- Systems of Linear Equations
- Mathematical Modeling
- Introduction to Quadratics
- Functions for Trigonometry
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Polynomial Functions Basics
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Circular Arcs, Circles & Angles
- Teaching Resources for High School Trigonometry