Law of cosines — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Law of cosines — a geometry concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 12
1959 AMC 12 Problem 36 • 1962 AMC 12 Problem 39 • 1963 AMC 12 Problem 34 • 1964 AMC 12 Problem 38 • 1967 AMC 12 Problem 32 • 1967 AMC 12 Problem 40 • 1981 AMC 12 Problem 21 • 1981 AMC 12 Problem 25 • 1982 AMC 12 Problem 23 • 1983 AMC 12 Problem 19 • 1984 AMC 12 Problem 27 • 1995 AMC 12 Problem 18 • 1998 AMC 12 Problem 26 • 2002 AMC 12A Problem 23 • 2002 AMC 12B Problem 23 • 2003 AMC 12B Problem 21 • 2006 AMC 12B Problem 23 • 2008 AMC 12B Problem 25 • 2009 AMC 12A Problem 13 • 2010 AMC 12A Problem 17 • 2012 AMC 12A Problem 16 • 2013 AMC 12A Problem 12 • 2013 AMC 12B Problem 24 • 2014 AMC 12A Problem 20 • 2016 AMC 12A Problem 21 • 2017 AMC 12A Problem 24 • 2018 AMC 12A Problem 20 • 2018 AMC 12B Problem 25 • 2019 AMC 12B Problem 25 • 2022 AMC 12A Problem 12 • 2022 AMC 12B Problem 19 • 2023 AMC 12B Problem 17 • 2023 AMC 12B Problem 20 • 2024 AMC 12A Problem 19 • 2025 AMC 12A Problem 8 • 2025 AMC 12A Problem 16 • 2025 AMC 12B Problem 21
AIME
1989 AIME Problem 6 • 1989 AIME Problem 10 • 1992 AIME Problem 13 • 1993 AIME Problem 15 • 2003 AIME I Problem 10 • 2003 AIME I Problem 12 • 2003 AIME II Problem 11 • 2004 AIME II Problem 11 • 2004 AIME II Problem 13 • 2005 AIME I Problem 7 • 2006 AIME II Problem 12 • 2009 AIME I Problem 15 • 2011 AIME II Problem 10 • 2012 AIME I Problem 12 • 2012 AIME I Problem 13 • 2012 AIME II Problem 13 • 2013 AIME I Problem 9 • 2013 AIME II Problem 5 • 2013 AIME II Problem 8 • 2013 AIME II Problem 13 • 2013 AIME II Problem 15 • 2014 AIME II Problem 12 • 2018 AIME I Problem 4 • 2018 AIME II Problem 12 • 2019 AIME I Problem 13 • 2019 AIME II Problem 11 • 2019 AIME II Problem 15 • 2021 AIME II Problem 5 • 2021 AIME II Problem 12 • 2022 AIME I Problem 11 • 2022 AIME I Problem 14 • 2024 AIME I Problem 10 • 2025 AIME I Problem 14 • 2025 AIME II Problem 12