SSA (side-side-angle)

Definition

SSA (Side-Side-Angle) is a condition in which two sides and a non-included angle of a triangle are known. It is also known as the ambiguous case because it can result in zero, one, or two possible triangles.

5 Must Know Facts For Your Next Test

1. SSA does not guarantee a unique triangle; there may be zero, one, or two possible solutions.
2. The Law of Sines is used to solve SSA configurations by relating the ratios of sides and angles.
3. If the given angle is acute and the opposite side is shorter than the adjacent side but longer than its height from the angle, two triangles are possible.
4. If the given angle is obtuse or right and the opposite side is less than or equal to the adjacent side, no triangle exists.
5. When solving SSA problems, always check for multiple solutions by considering different cases based on side lengths and angles.

Review Questions

• What does SSA stand for in trigonometry?
• How many possible triangles can be formed with an SSA configuration?
• What tool do we use to determine if multiple triangles exist in an SSA condition?

Related terms

Law of Sines: A formula that states $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ for any triangle with sides $a$, $b$, $c$ opposite angles $A$, $B$, $C$ respectively.

Ambiguous Case: Another term for SSA, highlighting that this configuration can lead to zero, one, or two possible triangles.

Non-right Triangle: A triangle where none of its interior angles are right angles (90 degrees).