SSS (side-side-side) triangle

Definition

SSS (side-side-side) triangle is a type of triangle where all three sides are known. This information allows the determination of all internal angles using the Law of Cosines.

5 Must Know Facts For Your Next Test

1. The Law of Cosines can be used to find each angle in an SSS triangle.
2. An SSS triangle is uniquely determined by its three side lengths.
3. The formula for the Law of Cosines is $c^2 = a^2 + b^2 - 2ab \cos(C)$, and similar formulas apply for finding other angles.
4. To solve for an angle using SSS, rearrange the Law of Cosines formula to isolate the cosine term.
5. Once one angle is found, other angles can be determined using either the Law of Cosines again or the Law of Sines.

Review Questions

• How do you use the Law of Cosines to find an angle in an SSS triangle?
• What makes an SSS triangle unique compared to other types of triangles?
• If given three sides of a triangle, explain how you would determine one interior angle.

Related terms

Law of Cosines: A formula relating the lengths of sides in a triangle to the cosine of one of its angles: $c^2 = a^2 + b^2 - 2ab \cos(C)$.

Law of Sines: A principle stating that $\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$ for any triangle.

Non-right Triangle: A triangle that does not have a 90-degree angle; requires different methods than right triangles for solving sides and angles.