In oblique triangle ABC, A = 34°, B = 68°, and a = 4.8. Find b to the nearest tenth.
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
Which of the following pairs of triangles can be proven congruent using the (Side-Angle-Side) criterion rather than the Law of Sines?
A
Two triangles with all three angles known to be equal in each triangle
B
Two triangles with all three sides known to be equal in each triangle
C
Two triangles with two angles and a non-included side known to be equal in each triangle
D
Two triangles with two sides and the included angle known to be equal in each triangle
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Verified step by step guidance1
Recall the SAS (Side-Angle-Side) congruence criterion: two triangles are congruent if two sides and the included angle (the angle between those two sides) of one triangle are respectively equal to two sides and the included angle of the other triangle.
Analyze each option to see if it fits the SAS criterion:
Option 1: Triangles with all three angles equal. This is Angle-Angle-Angle (AAA), which shows similarity but not congruence, so SAS does not apply here.
Option 2: Triangles with all three sides equal. This is Side-Side-Side (SSS) congruence, which is a different criterion from SAS.
Option 3: Triangles with two angles and a non-included side equal. This is Angle-Angle-Side (AAS), which is not SAS because the side is not between the two angles.
Option 4: Triangles with two sides and the included angle equal. This matches the SAS criterion exactly, so these triangles can be proven congruent using SAS.
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