Investigation: Exploring the Sine Law
Completion requirements
| Investigation |
Exploring the Sine Law
Open the Sine Law applet to begin exploring this relationship. Use the applet to answer the following questions.
Move the points to see how the ratios of the sine of an angle and the side length across from it are related
- How are angle \(A\) and side \(a\) related? How about angle \(B\) and side \(b\)? Angle \(C\) and side \(c\)?
- How are the ratios \(\frac{{\sin A}}{a},\thinspace \frac{{\sin B}}{b},\thinspace {\rm{and}}\frac{{\sin C}}{c}\) related? Move the points around to see if this relationship holds for different triangles.
Key Lesson Marker |
The Sine Law
The sine law states that in a non-right angle triangle, the sides and angles are related in a way such that:
\[\begin{array}
\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}} \\
\end{array}\]
OR
\[\begin{array}
\frac{{\sin A}}{a} = \frac{{\sin B}}{b} = \frac{{\sin C}}{c} \\
\end{array}\]
\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}} \\
\end{array}\]
OR
\[\begin{array}
\frac{{\sin A}}{a} = \frac{{\sin B}}{b} = \frac{{\sin C}}{c} \\
\end{array}\]
- Determining a side when you are given the angle opposite the unknown side and another side and its opposite angle (Figure 1).
- Determining an angle when you are given the side opposite the unknown angle and another side and its opposite angle (Figure 2).
