look at the ratio a/b as the alpha increases.

a/b = 0 when alpha is zero
a/b = 1 when alpha is 90
a/b = infinity when alpha is 180

ie when b does not exist ratio does not exist.

thus infinity tells that some assumption/rule in the calculation is no longer valid. here, the structure is nolonger a triangle.

also note the transition from zero to one and then a jump to infinity!