2019 AMC 10C Problems/Problem 2

For this problem we shall start by computing the total number of triangles. There are

\[\bimom{5}{3}\] (Error compiling LaTeX. Unknown error_msg)

ways to choose 3 verticies to form a triangle and of these 10 triangles only 5 are obtuse triangles. We can do this by either counting them individually or noting that there are 5 options for the middle vertex. Thus the answer is

\[\frac{1}[2}\] (Error compiling LaTeX. Unknown error_msg)