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.