Two trains leave a station on different tracks. The tracks make an angle of 115° with the station as a vertex. The first train travels 200 kilometers and makes its first stop in Pocomoc, while the second train travels 350 kilometers and makes it first stop in Easton. How far apart are the trains when both are at their first stop? Round the answer to the nearest tenth.
The trains and the station form a triangle with sides 200 km and 350 km enclosing an angle of 115°. Use the law of cosines: d² = 200² + 350² − 2(200)(350)cos(115°) ≈ 221,666.5. Taking the square root gives d ≈ 470.8 km, so the trains are about 470.8 km apart.
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