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A detailed tutorial on the Law of Tangents. Step by step tutorial including several examples of the Law of Tangents for reference.

The Law of Tangents refers to the lengths of the three sides of a triangle and the tangents of the angles. This can be used with respect to any triangle, not just right triangles. While the Law of Tangents is not as well known as the Law of Sines or the Law of Cosines, it is useful. The Law of Tangents can be used whenever either two sides and an angle, or two angles and a side, are known on any given triangle. The proof of this law starts with the Law of Sines. The Law of Tangents is as follows:

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A detailed tutorial on the ambiguous case. Step by step tutorial including several example problems of the ambiguous case for reference.

An ambiguous case is actually any case in mathematics that is open to more than one interpretation, or has more than one solution. There are many different examples of an ambiguous case. However, what most people refer to as the ambiguous case is the Law of Sines. The Law of Sines can use many different techniques to be solved, and those techniques can also be used to figure out if two triangles are congruent.

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A detailed tutorial on the the Law of Sines and how to prove the Law of Sines. Step by step tutorial including several examples of how to solve problems with the Law of Sines for reference.

The Law of Sines is a formula that can be used when a triangle has both side and angle measures. The Law of Sines is expressed as:

Where a, b, and c represent the sides, and A, B, and C represent the angles that are opposite of those sides. This formula looks very similar to the Pythagorean Theorem.