SAS (side-angle-side) triangle

Definition

SAS (Side-Angle-Side) triangle is a type of triangle where two sides and the included angle are known. This information can be used to determine other properties of the triangle using trigonometric laws.

5 Must Know Facts For Your Next Test

1. The Law of Cosines is often used to find the unknown side or angle in an SAS triangle.
2. In an SAS triangle, the known angle is always between the two given sides.
3. The formula for the Law of Cosines is $c^2 = a^2 + b^2 - 2ab \cos(C)$, where $C$ is the included angle.
4. SAS configuration ensures that there is only one unique solution for the triangle, eliminating ambiguity.
5. SAS triangles can be used to solve real-world problems involving distances and angles.

Review Questions

• What information do you need to apply the SAS condition in a triangle?
• How does the Law of Cosines help in solving an SAS triangle?
• In an SAS triangle with sides $a$, $b$, and angle $\gamma$ between them, write down the equation to find side $c$.

Related terms

Law of Cosines:

A rule stating that for any triangle with sides $a$, $b$, and $c$, and corresponding opposite angles $A$, $B$, and $C$: $$c^2 = a^2 + b^2 - 2ab \cos(C)$$

Law of Sines:

A rule stating that for any triangle, the ratio of a side length to the sine of its opposite angle is constant: $$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$$

SSA Triangle: A type of triangle where two sides and a non-included angle are known. This configuration can sometimes result in more than one valid solution.