Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
1. Measuring Angles
Complementary and Supplementary Angles
3:47 minutes
Problem 25
Textbook Question
Textbook QuestionThe measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 147° 12' , 30° 19'
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Triangle Angle Sum Theorem
The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees. This fundamental principle allows us to determine the measure of an unknown angle when the measures of the other two angles are known. In this case, by adding the two given angles and subtracting from 180°, we can find the third angle.
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Solving Right Triangles with the Pythagorean Theorem
Angle Measurement in Degrees and Minutes
Angles can be measured in degrees, and sometimes in minutes and seconds for greater precision. One degree is divided into 60 minutes, and one minute is further divided into 60 seconds. When calculating the third angle, it is essential to correctly add or subtract these measurements, ensuring that the conversion between degrees and minutes is handled properly.
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Reference Angles on the Unit Circle
Conversion of Angle Units
When working with angles expressed in degrees and minutes, it may be necessary to convert between these units for calculations. For example, to convert minutes to degrees, divide the number of minutes by 60. Understanding how to perform these conversions is crucial for accurately determining the measure of the third angle in the triangle.
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Coterminal Angles on the Unit Circle
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