Triangles: The Side-Angle Relationship


Triangles: The Side-Angle Relationship



What is the relationship between side B and angle x in the triangle below?



Remember that the interior angles of a triangle add up to 180 degrees.


In this triangle, we then have 90
 + 60 + x = 180
=> 150 + x = 180
=> x =180 - 150
=> x = 30

So, the smallest angle is opposite the shortest side. 



Let's look at another one:


What is the relationship between side B and angle y?



 40 + 25 + y = 180
=> 65 + y = 180
=> y = 115

The largest angle is opposite the longest side.



These side-angle relationships are true for all types of triangles.