Non-Right Triangles Study Sheet

Definitions

• The Law of Cosines defines the relationship between any angle in a triangle and the two sides adjacent to it. The formula is: a² = b² + c² – 2bc cosA
• The Law of Sines defines the relationship between the sine of any angle in a triangle and the side opposite it. The formula is: a/sinA = b/sinB = c/sinC
• The Law of Sines Ambiguous Case refers to the scenario where the angle in question may have one of two possible solutions.
• A Oblique Triangle is a triangle without any right angles.
• A Right Angle is an angle that measures 90 degrees, and is formed by two perpendicular lines.
• The Sum of the Angles of any triangle is always 180 degrees. Oblique Triangle

Solving an Oblique Triangle

The tools and techniques you use to solve an oblique triangle will depend on what information about the triangle you have.

Use the scenarios listed below to determine how to go about finding your unknowns:

If you know all three sides:

• Use the Law of Cosines and plug in the values for the sides a, b, and c
• Solve for angle A
• Use the angle value with the Law of Sines to find angle B
• Use the Sum of the Angles with the two angles to find angle C

If you know two sides and the angle between them:

• Use the Law of Cosines and plug in the values for the sides b, c, and the angle A
• Solve for side a
• Use the angle value with the Law of Sines to find angle B
• Use the Sum of the Angles with the two angles to find angle C

If you know two angles and any side:

• Use the Sum of the Angles with the two angles to find the third angle
• Use the Law of Sines and plug in the values for the two angles and the side
• Solve for the side
• Use the Law of Sines with an angle, the side opposite it, and the angle opposite the side you still don’t know to find that side