In trigonometry, the law of sines is an equation relating the lengths of the sides of any shape triangle to the sines of its angles:
$$\frac{a}{\sin\alpha }=\frac{b}{\sin\beta }=\frac{c}{\sin\gamma}=2R$$
where,
a, b, cβ sides of a triangle;
α, β, γβ angles of a triangle;
Rβ radius of the triangle's circumcircle.
The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known β a technique known as triangulation. It can also be used when two sides and one of the non-enclosed angles are known. In some such cases, the triangle is not uniquely determined by this data (called the ambiguous case) and the technique gives two possible values for the enclosed angle. In a Euclidean space, the sum of angles of a triangle equals the straight angle (180 degrees, Ο radians, two right angles, or a half-turn)
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Frequently asked questions
What is the law of sines used for?
The law of sines is used to find unknown sides or angles in a triangle when enough side-angle information is known.
When can you apply the law of sines?
You can apply it when you know two angles and one side, or two sides and a non-included angle.
What is the ambiguous case in the law of sines?
The ambiguous case happens when two different triangles can satisfy the same side-side-angle data.
