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Solving Oblique Triangles

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There are four categories of oblique triangles that can be solved and whose names express what is known about the side lengths and angle measurements.

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An SAA triangle is one where the length of one side is known together with the measures of an adjacent angle and an opposite angle.

An SSA triangle is one where the measure of an angle is known together with the lengths of an adjacent side and an opposite side.

An SAS triangle is one where the lengths of two sides are known together with the measure of the included angle

And finally an SSS triangle is one where the lengths of all three sides are known.

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Contributed by: Eric Schulz (March 2011)
Open content licensed under CC BY-NC-SA

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To solve an oblique triangle means to find the lengths of the unknown sides and the measures of unknown angles. If two angles are known, then the third angle can be determined simply by knowing that the sum of the three interior angles must equal . Both the law of sines and the law of cosines are important tools for solving oblique triangles.

law of sines:InlineMathlaw of cosines:InlineMathColumns=Columns

In the case of the SSS triangle, there is an option to show and compute the enclosed area of the triangle as an application of Heron's formula.

The Demonstration allows you to investigate the four categories of oblique triangles, create examples that can be "solved" manually with paper, pencil, and calculator, and then easily have the lengths and measures of unknown sides and angles be displayed for verification of the manual solutions. In the category SSA the visual will demonstrate why there are at times two possible triangles rather than just one.

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