Choose the law and the formula that would be used to solve the triangle.

Key takeaway: When solving a triangle, the first decision is whether the situation calls for the Law of Sines or the Law of Cosines. The choice depends on the given sides and angles.

To solve a triangle, choose the law that matches the information given.

Correct law

Law of Sines

Correct formula

$$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$$

From the options shown, the matching formula is

$$\frac{\sin A}{a}=\frac{\sin C}{c}$$

and the law is the Law of Sines.

Why

The Law of Sines is used when you know at least one angle-side opposite pair, which is the standard setup for many triangle-solving problems.

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Pitfalls the pros know 👇 Do not choose the Law of Cosines unless you have SAS or SSS information. A common mistake is matching the wrong formula with the correct law.

What if the problem changes? If the triangle were given with two sides and the included angle, then the Law of Cosines would be the better first choice. If one angle and its opposite side are known, the Law of Sines is usually used first.

Tags: Law of Sines, triangle solving, opposite sides