Law of Sines

Definition: The law of sines is used to find unknown sides or angles of a triangle. The formula is made up of the following ratios:

The law of sines can only be used when the following information is available:

One side length and its opposite angle measure is known


One or more other sides lengths or angle measures is known


Find the missing angles and sides:


Step 1: Plug the given information into the law of sines formula, where ∠A = 35, ∠B = 125 and side b = 7.

Step 2: Working with the first two ratios, solve the proportion to find side a:

Step 3: To find the measure of ∠C, we can use the Triangle Angle Sum Theorem (the sum of a triangle’s interior angles always totals 180°):

∠C = 180 – 125 – 35 = 20°

Step 4: To find side c, we can set up the following proportion and solve:

Still need help using the Law of Cosines? Download Yup and get help from an expert math tutor 24/7.