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
7. Non-Right Triangles
Law of Cosines
4:56 minutes
Problem 15a
Textbook Question
Textbook QuestionIn Exercises 13–16, find the area of the triangle having the given measurements. Round to the nearest square unit. a = 2 meters, b = 4 meters, c = 5 meters
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Triangle Area Formulas
The area of a triangle can be calculated using various formulas, with one of the most common being Heron's formula. This formula is particularly useful when the lengths of all three sides are known. It states that the area can be found using the semi-perimeter (s) and the side lengths (a, b, c) as follows: Area = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2.
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Heron's Formula
Heron's formula allows for the calculation of a triangle's area when the lengths of all three sides are known. By first calculating the semi-perimeter, which is half the sum of the side lengths, one can then apply the formula to find the area. This method is particularly advantageous when height is not readily available, making it a versatile tool in trigonometry.
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Properties of Triangles
Understanding the properties of triangles, including the triangle inequality theorem, is essential for determining the feasibility of a triangle with given side lengths. The theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. This ensures that the specified dimensions can indeed form a valid triangle, which is a prerequisite for calculating its area.
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