2002 #6 and 36

Some triangle work and a bitchin' series!

Difficulty: Simple triangle rules.

Difficulty: Just algebra. Looks much worse than it is.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 06 and answer 36.