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Triangle Side and Angle Inequalities - Problem 1

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

The angle opposite the smallest side of a triangle has the smallest measure. Likewise, the angle opposite the largest side has the largest measure. So, if given three side lengths, in order to put the angles in order from smallest to largest, first find the smallest angle by finding the angle opposite the smallest side, then, the medium-sized angle by finding the angle opposite the medium-sized side, and the largest angle opposite the largest side. Thus, it is possible to find a relationship between the angles of a triangle even if the exact measurements are unknown.

In this problem we’re being asked to list the angles of this triangle in order from smallest to largest. The only thing we need to look at here is how long are the sides? Let’s start by finding the small side. Well it’s pretty clear that 1.3 is the small side in this triangle and that is opposite angle S. So if I’m starting with my smallest angle I’m going to say measure of angle S is my smallest.

The next small side is 2.6. 2.6 is opposite angle R so we have measure of angle S the next largest is measure of angle R and by process of elimination we see that 2.7, our longest side is opposite of angle Q. So the key to these problems is you’re saying which side is the shortest, which side is the longest and listing them in order.

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