In triangle , = cm, = and = . Find the length of side , to the nearest centimeter.
Table of contents
- 0. Review of College Algebra4h 43m
- 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
- OLD 1. Angles and the Trigonometric Functions Coming soon
- OLD 2. Trigonometric Functions graphs, Inverse Trigonometric Functions Coming soon
- OLD 3. Trigonometric Identities and Equations Coming soon
- OLD 4. Laws of Sines, Cosines and Vectors Coming soon
- OLD 5. Complex Numbers, Polar Coordinates and Parametric Equations Coming soon
- NEW (not used) 7. Laws of Sines, Cosines and Vectors Coming soon
- NEW (not used) 8. Vectors Coming soon
- NEW(not used) 9. Polar equations Coming soon
- NEW (not used) 11. Graphing Complex Numbers Coming soon
7. Non-Right Triangles
Law of Sines
Multiple Choice
Given triangle ABC with sides , , and opposite angles , , and respectively, which expression represents the approximate length of side using the Law of Sines?
A
B
C
D
0 Comments
Verified step by step guidance1
Recall the Law of Sines, which states that in any triangle ABC, the ratio of the length of a side to the sine of its opposite angle is constant: \(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\).
To find an expression for side \(a\), start from the equality \(\frac{a}{\sin(A)} = \frac{b}{\sin(B)}\) since it relates side \(a\) and side \(b\) with their opposite angles.
Rearrange this equation to solve for \(a\) by multiplying both sides by \(\sin(A)\): \(a = \frac{b}{\sin(B)} \times \sin(A)\).
Write the expression clearly as \(a = \frac{b \cdot \sin(A)}{\sin(B)}\) to represent the length of side \(a\) in terms of side \(b\) and the sines of angles \(A\) and \(B\).
This formula allows you to calculate the approximate length of side \(a\) if you know the length of side \(b\) and the measures of angles \(A\) and \(B\).
Related Videos
Related Practice
Multiple Choice

