Sophisticated, beautiful, smart and talented: it's no wonder Rin Tohsaka is considered the school idol. She even earns the nickname "miss perfect" among some. Yet she always seems distant and goes home right after school. For Shiro, finding out Rin was a magus was only part of the surprise. It was even more of a shock to find out the idol he had adored from afar was loud, easy to anger and a slightly wicked; particularly when dealing with him. However as much as Rin likes to tease Shiro, there are subtle hints that she likes him and on occasion her teasing backfires and she ends up being embarrassed herself.
Rin maintains a cheerful friendly persona, making her very popular at school - something she considers a part of maintaining the good name of the Tohsaka family. At first Shiro is disheartened by her image being an act, but as he gets to know her better, he finds she truly a good person with a kind heart - just not in the package he expected. With all these traits going for her, it's not surprising that more than a few people in the story are jealous of her. Despite her abilities and confidence, Rin has one bad trait she's self concious about: she has the tendency to screw up important things at a crucial moment.
The Tohsaka family has participated in the grail war since the beginning. Rin is only the latest in a long lineage of Tohsaka mages. Her magic training has been tough, but Rin has no regrets about fulfilling her destiny. In fact she enjoys it. Her secret weapon are gems she uses to store magic energy. She's spent years slowly charging them for the time when they'll be needed. This allows her to wield magic normally beyond her potential.
Rin originally intended to summon the strongest class of servant, Saber; but instead ended up with the cynical Archer. It's not clear if this is because she screwed up at the last moment during the summoning, or if it's because she coincidentally had an item that linked her to him. Archer is very good at annoying the hell out of Rin, often unintentionally. She introduces herself to him using her full name, and on a whim Archer decides to call her Rin (instead of Tohsaka as would be customary in Japanese), much to her annoyance. While the two argue a lot, when it comes to the grail war they make a good team.
I determine whether or not something is possible.