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:

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

One side length and its opposite angle measure is known

AND

One or more other sides lengths or angle measures is known

Example:

Find the missing angles and sides:

Solution:

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:

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