 SSS Triangles are triangles where all three sides are known. The angles inside might be unknown, but they can be determined by following three steps. Understanding SSS triangles and how to solve to find the angles can be beneficial in a variety of situations outside of math class, like when precise angles are needed for building something.

The Basics of Triangles

Triangles have certain rules which make it easier for a student to find any angle or side based on what they already know. With SSS triangles, 3 sides are already known, so the student can use the steps below to determine what all of the angles are to solve the triangle. Because of these basic rules, a student just needs to know one formula and how it can be rearranged to find the angles.

Three Steps to Find the Angles of an SSS Triangle

To find the angles of an SSS triangle, the student should follow three steps, one for each angle. The first is to use the Law of Cosines to determine one of the angles. It’s typically a good idea to work on the largest angle first. Then, they can use the Law of Cosines to find another angle. Finally, finding the third angle is a matter of adding the first two together and subtracting from 180.

The Law of Cosines

The Law of Cosines states that c^2=a^2+b^2-2ab cos(C). When the numbers are all plugged in, this can be used for sides and angles of triangles. However, for the SSS triangle, it needs to be used to find the first angle when all three sides are known. In this instance, it’s helpful to start with the formula rearranged slightly. To solve for angle C first, use the formula: cos(C)=(a^2+b^2-c^2)/2ab. It can be rearranged to find other angles as well.

Use the Law of Cosines Again

Once the first angle has been found, the student can use the same law to find a second angle. For angle B, they’ll want to use the formula cos(B)=(c^2+a^2-b^2)/2ca. To solve for angle A, they’ll want to use the formula cos(A)=(b^2+a^2-c^2)/2bc. Basically, these are the same as the formula in the previous step, but they have been rearranged to make it a better starting point based on the angle the person wants to solve for. They can be used in any order, and it’s only necessary to use the Law of Cosines twice.

Add and Subtract for the Last Angle

The angles in a triangle always add to 180 degrees, no matter what type of triangle it is. Once a student knows two of the angles, they can add these together and subtract from 180 to determine what the final angle is. At this point, they will know all 3 sides and all 3 angles for the triangle.

Learning how to find the angles in a triangle can be beneficial in a variety of situations. Taking the time to learn the Law of Cosines and how it can be rearranged to make finding an angle easier can make it possible for a student to solve any SSS triangle. Practice a few problems today to get a little more experience working with SSS triangles now.