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Trigonometry

Course: Trigonometry > Unit 3

Lesson 1: Law of sines
Math
Trigonometry
Non-right triangles & trigonometry
Law of sines
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Non-right triangles & trigonometry: FAQ

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Frequently asked questions about non-right triangles & trigonometry

What is the law of sines?

The law of sines is a formula that can be used to solve any triangles, not just right triangles.
The law of sines states that in any triangle, the ratio of the sine of an angle to the opposite side length is equal for all three angles and sides. It looks like this:
start fraction, sine, left parenthesis, A, right parenthesis, divided by, a, end fraction, equals, start fraction, sine, left parenthesis, B, right parenthesis, divided by, b, end fraction, equals, start fraction, sine, left parenthesis, C, right parenthesis, divided by, c, end fraction
Where A, B, and C are the angle measures of the triangle, and a, b, and c are the opposite side lengths.
Practice with our Solve triangles using the law of sines exercise.

What is the law of cosines?

The law of cosines states that in any triangle, the square of a side is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the opposite angle. It looks like this:
a2=b2+c2−2bccos⁡(A)b2=a2+c2−2accos⁡(B)c2=a2+b2−2abcos⁡(C)\begin{aligned} a^2 &= b^2 + c^2 - 2bc \cos{(A)}\\\\ b^2 &= a^2 + c^2 - 2ac \cos{(B)}\\\\ c^2 &= a^2 + b^2 - 2ab \cos{(C)} \end{aligned}
Practice with our Solve triangles using the law of cosines exercise.

What does it mean to solve a "general triangle"?

Solving a "general triangle" means finding all of its side lengths and angle measures. In some cases, we might only need to find one or two missing pieces of information, but in other cases we might need to find all six. The law of sines and the law of cosines can help us with this.
Practice with our General triangle word problems exercise.

How do we choose between using the law of sines and the law of cosines to solve a triangle?

It depends on what pieces of information we already know! If we know two sides and the angle between them, we'll use the law of cosines to find the third side. If we know two angles and one side, we'll use the law of sines to find the other two sides.
Check out our Trig word problem: stars video.
Check out our Laws of sines and cosines review article.

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