USAAAO — 2023 First Round
Questions 17–18
The fictional towns of Baia and Caia are located at (66.56° N, 67.55° E) and (δ, 18.95° E), respectively. It is known that the spherical triangle with vertices at Baia, Caia, and the North Pole covers 6.75% of Earth's surface. Compute δ.
Now suppose that Lucas is standing still in Baia (from the previous question), and Justin is standing still on the equator. Let PL1 and PJ1 be the paths of Lucas's and Justin's shadows on the summer solstice, respectively. Let PL2 and PJ2 be the paths of Lucas's and Justin's shadows on the vernal equinox, respectively. Assume that the heights of Lucas and Justin are small compared to the radius of the Earth, there is no atmospheric refraction, and that the Sun is a point. Given Earth's obliquity ε = 23.44°, which of the following is the most specific accurate description of the shapes of each path?
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Answer both parts to check. Both must be correct to count as correct.
Source
USAAAO 2023 First Round. Question text, choices, and answer were transcribed from the official USAAAO exam and solutions PDFs.