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 Sines
Problem 7.3a
Textbook Question
Textbook QuestionIn each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?
a. two triangles
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Triangle Formation
A triangle is formed when three points are connected by line segments. In this context, one point is fixed, and the other two points are determined by the intersection of the line segment with the x-axis and the vertical line from the fixed point. Understanding how varying the length L affects the angles and sides of the triangle is crucial for determining the conditions under which two triangles can be formed.
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Geometric Constraints
Geometric constraints refer to the limitations imposed by the positions of points and the lengths of segments in a geometric figure. In this scenario, the length L must be such that it allows the line segment to intersect the x-axis at two distinct points, creating two separate triangles. Analyzing these constraints helps in identifying the specific values of L that satisfy the conditions for triangle formation.
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Trigonometric Ratios
Trigonometric ratios, such as sine, cosine, and tangent, relate the angles of a triangle to the lengths of its sides. In the context of this problem, these ratios can be used to analyze the relationships between the angles formed by the line segment and the x-axis. Understanding these ratios is essential for determining the possible values of L that allow for the creation of two triangles, as they dictate the angles and thus the triangle's properties.
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