How to Calculate Oblique Triangles

The sum of all the angles in an oblique triangle is 180 degrees.

Oblique triangles contain no right angles. Unlike right triangles, oblique triangles are not solvable using techniques such as the Pythagorean Theorem. Triangles consist of six parts: three sides and three angles. If you know the length of at least one side and two other parts of the triangle, you can use the Law of Cosines and the Law of Sines to determine the other parts or solve the triangle.

Instructions

1. Specify names for each part of your triangle. For example, you can call the three angles "A," "B" and "C" and the three sides "a," "b" and "c."

2. Plug your three known sides into the Law of Cosines. The Law of Cosines is a^2 = b^2 + c^2 - 2*b*c*cos(A).

3. Solve the angle "A" as arccos ( (a^2 - b^2 - c^2) / (2*b*c) ) = A.

4. Use the Law of Sines to solve the remaining parts of the triangle. The Law of Sines is a / sin(A) = b / sin(B) = c / sin(C).

5. Solve "B" to be B = arcsin ( ( b*sin(A) ) / a).

6. Solve C to be either arcsin ( (c*sin(B) / b) ) or arcsin ( ( c*sin(A) ) / a ).

7. Check your calculations. If the three angles of the triangle add up to 180 degrees, your calculations are correct.

References

• SparkNotes: Solving Oblique Triangles
• Clark College: Oblique Triangles