The Law of Sines isn’t too hard if you know the formula. Sure, you have to know more than just SohCahToa? But you can do it! First, this page gives you the formula. Then, it explains how to use the formula if you are given two angles and a side. Next, it explains how to use the formula if you are given two sides and an angle. Last, is a downloadable page you can print with all this information.
Law of Sines Formula
Now that you know what the Law of Sines Formula is, let’s use it for solving triangles! If you’re given two angles and a side (ASA or AAS), see the first given. If you’re given two sides and one angle (SSA), hold on to your horses, because it’s going to be a bumpy ride in the second given.
Given: 2 Angles and 1 Side (ASA or AAS)
Given: 2 Sides and 1 Other Angle (SSA)
1. Find the Height
Multiply the sin of the given angle (A) by the adjacent side (b).
Hint: You might want to relabel the sides and angle you are given.
2. Compare Sides and Height
Is the adjacent side (b) greater than the opposite side (a)? Is the opposite side (a) greater than the height (h)?
3. Compare Opposite Side and Height
Is the height (h) greater than the side opposite (a) the given angle?
4. Two Triangles Exist: The Acute Triangle
Find the angle (B1) across from the adjacent side by using law of sines.
5. Two Triangles Exist: The Obtuse Triangle
Find the angel (B2) across from the adjacent side.
Law of Sines Printout
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Beyond Solving Triangles…
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