Today’s SAT question of the day is a geometry question about a triangle that isn’t even shown on the test.  This triangle, however, is shown. They tell us that this one (ABC) is congruent to mysterious triangle DEF.

They would like to know what one of the side lengths of DEF must be. While the Pythagorean theorem would get us to that answer, remembering our 30-60-90 triangle will be even faster.

BC is the hypotenuse, and it’s 12 units long. That makes AB, the side opposite the 30 degree angle, 6. AC, then, is 6√3.  Since ABC is congruent to DEF, the options for DEF’s side lengths are the same: 6, 6√3, and 12.

For this problem, choice D gives us the right answer. For similar problems, remembering your special right triangles will save you a lot of time on test day – they’re printed in your test book if you have a momentary lapse, but do try to memorize them!