Problem 24 (2024 AMC 8)
AMC 8Hard
From module Geometry Basics
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Understand the scale
Scale
0.5: Easiest math competition problems, often solvable even for early middle school students without experience.
1: Problems strictly for beginners, often at a moderate middle school level.
1.5: Problems for stronger beginner students, on the level of the middling problems in most middle school contests.
2: For motivated beginners, harder questions from the previous categories.
2.5: More advanced beginner problems, hardest questions from previous categories.
3: Early intermediate problems that require more creative thinking.
3.5: Tougher early intermediate problems that consistently stretch into higher-level creative thinking or conceptual knowledge.
4: Intermediate-level problems.
4.5: Upper intermediate problems approaching the upper bound for non-invitational sprint math competitions.
5: More difficult AIME problems or simple proof-based Olympiad-style problems.
6: High-level AIME-styled questions or introductory Olympiad-level questions.
7: Tougher Olympiad-level questions, may require more technical knowledge.
8: High-level Olympiad-level questions.
9: Expert Olympiad-level questions.
9.5: The hardest problems appearing on Olympiads which the strongest students could reasonably solve.
10: Historically notorious problems, generally unsuitable for even very hard competitions because they are exceedingly tedious, long, and difficult.
Right TrianglesAreaCoordinate Geometry
Problem
Jean made a piece of stained glass art in the shape of two mountains, as shown in the figure below. One mountain peak is feet high and the other peak is feet high. Each peak forms a angle, and the straight sides of the mountains form with the ground. The artwork has an area of square feet. The sides of the mountains meet at an intersection point near the center of the artwork, feet above the ground. What is the value of ? [See figure in original PDF]
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