2003 AIME I Problems/Problem 10
Problem
Triangle is isosceles with
and
Point
is in the interior of the triangle so that
and
Find the number of degrees in
Solution
From the givens, we have the following angle measures: ,
. If we define
then we also have
. Then Apply the Law of Sines to triangles
and
to get
Clearing denominators, evaluating and applying one of our trigonometric identities to the result gives
and multiplying through by 2 and applying the double angle formula gives
and so
and, since , we must have
, so the answer is
.
See also
2003 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |