Problems Section: Problems 1311 - 1320

Q1311 Prove that $\tan75^{\circ}-\tan60^{\circ}=2$ using purely geometrical arguments.

Q1312 Three right-angled triangles have integral side lengths. The side lengths of the first and second triangles are, respectively, 5, 12, 13, and 8, 15, 17 (units). Given that the length of the hypotenuse of the third triangle is 221 units, find the other two lengths.
 
Q1313 This year (2009), November 13th falls on Friday. Explain why every year must have at least one Friday the thirteenth. What is the largest number of these days that can fall in a year?