Given two triangles, and , where side corresponds to and side corresponds to , if , , , and , what value of will make the triangles similar by the SAS similarity theorem?
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 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
Multiple Choice
According to the Law of Sines, under which of the following angle conditions could a triangle exist? Select the correct option.
A
The sum of the three angles is .
B
The sum of the three angles is less than .
C
The sum of the three angles is and each angle is greater than .
D
One angle is .
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Verified step by step guidance1
Recall the fundamental property of triangles: the sum of the three interior angles must be exactly \(180^\circ\).
Understand that the Law of Sines applies to any triangle, but for a triangle to exist, each angle must be greater than \(0^\circ\) and less than \(180^\circ\).
Evaluate the given conditions: if the sum of angles is \(200^\circ\), it violates the triangle angle sum property, so no triangle can exist.
If the sum of angles is less than \(180^\circ\), it also violates the triangle angle sum property, so no triangle can exist.
If one angle is \(0^\circ\), the figure is not a triangle because an angle of zero means no interior angle at that vertex, so no triangle can exist.
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