Assuming the arch is a perfect triangle, the distance from the base of the arch can be calculated using the law of sines. The angle of 7.31° is opposite the side of the triangle with length 192 m. The other two sides of the triangle are the distance from the base of the arch and the line of sight.
Distance = (192 m * sin(7.31°)) / sin(90°)
Distance = 0.9 km
You are driving into St. Louis, Missouri, and in the distance you see the famous Gateway-to-the-West arch. This monument rises to a height of 192 m. You estimate your line of sight with the top of the arch to be 7.31 ° above the horizontal. Approximately how far (in kilometers) are you from the base of the arch?
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