I came up with this code although it is buggy. I think that the triangles are supposed to be the same size. The triangles are just supposed to be random using the import random module I wasn't given specifics about the size. She just said she needs 75 of them. Based on the example problem I configured this code.
I'm not sure how to configure the loop so I can set the points/coordinates for a triangle using an array
import arcpy
import random
env = the path lol
feat = 'triangles.shp'
polygon_list = []
#I will create random triangles across the world shapefile using the random module
for y in range (90,0,-10):
for x in range(-180,180,10):
cornersArray = arcpy.Array()
p1 = arcpy.Point()
p1.X = x
p1.Y = y
cornersArray.add(p1)
p2 = arcpy.Point()
p2.X = x + 10
p2.Y = y
cornersArray.add(p2)
p3 = arcpy.Point()
p3.X=x+10
p3.Y = y-10
cornersArray.add(p3)
poly = arcpy.Polygon(cornersArray)
polygon_list.append(poly)
#I will copy the features in my list to the triangle shapefile
arcpy.CopyFeatures_management(polygon_list,feat)
#I will define the projection for the triangles shapefile
arcpy.DefineProjection_management(feat,arcpy.SpatialReference(4326))
print 'Finished created the triangles'