2008 iTest Problems/Problem 57
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Problem
Let a and b be the two possible values of given that . If , where and are relatively prime positive integers, compute .
Solution
Let . Multiply both sides by to get Let . Using the sum formula for tangent, the sum of the two possible values of is If a triangle has opposite side and hypotenuse , by the Pythagorean Theorem, the adjacent side's length is . That means if , then . That means . Therefore, the sum of the two possible values of is Thus, .
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 56 |
Followed by: Problem 58 | |
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