Which of the following sets of angles can form a triangle?
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
In triangle , the measure of angle is , and side is equal to side . What is the measure of angle ?
A
B
C
D
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Verified step by step guidance1
Identify the given information: In triangle ABC, angle A measures 58\(\degree\), and sides a and c are equal in length.
Recall that in a triangle, sides opposite equal angles are equal. Since sides a and c are equal, the angles opposite these sides must also be equal. Therefore, angle B equals angle C.
Use the triangle angle sum property, which states that the sum of the interior angles of a triangle is 180\(\degree\). Write the equation: \(A + B + C = 180\degree\).
Substitute the known values and relationships into the equation: \(58\degree + B + C = 180\degree\), and since \(B = C\), rewrite as \(58\degree + C + C = 180\degree\) or \(58\degree + 2C = 180\degree\).
Solve for angle C by isolating it: \(2C = 180\degree - 58\degree\), then \(C = \frac{180\degree - 58\degree}{2}\). This will give the measure of angle C.
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