Non-right triangles

Definition

Non-right triangles are triangles that do not have a 90-degree angle. Solving these triangles often involves using trigonometric laws such as the Law of Sines or the Law of Cosines.

5 Must Know Facts For Your Next Test

1. The Law of Sines states that the ratios of the lengths of sides to the sines of their opposite angles are equal in any triangle: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$.
2. The Law of Cosines, useful for solving non-right triangles, is given by: $$c^2 = a^2 + b^2 - 2ab \cos(C)$$.
3. Ambiguous Case (SSA) occurs when two different triangles can be created with given data, requiring careful analysis.
4. For an obtuse triangle, one angle measures greater than 90 degrees.
5. The sum of all internal angles in any triangle is always 180 degrees.

Review Questions

• What is the formula for the Law of Sines?
• How do you apply the Law of Cosines to find a missing side in a non-right triangle?
• What is the ambiguous case in solving non-right triangles?

Related terms

Law of Sines: A mathematical relationship stating that the ratio between the length of a side and the sine of its opposite angle is constant for all three sides and angles in a triangle.

Law of Cosines: A formula used to calculate one side or angle in any triangle, given two sides and their included angle or three sides: $$c^2 = a^2 + b^2 - 2ab \cos(C)$$.

Ambiguous Case: A situation in triangle solving where given two sides and a non-included angle (SSA), there may be two possible solutions, one solution, or no solution.