1999 AMC 12 Problem 27
Attempt Problem 27 of the 1999 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1999 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
In triangle and Then in degrees is
Answer: A
Small hint:
Square both equations and add them
Big hint:
Use to get then rule out one case
Solution:
Squaring both equations and adding gives so and
Then so or If then making a contradiction. Hence
Thus, the correct answer is A.
Problem 27 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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- 1958 AMC 12
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- 1998 AMC 12