A surveying team is on a mission to confirm the estimated altitude of a mountain on an island in the central Pacific. (There are worse jobs in this world.) One of the team's interns has accidentally damaged their altitude-finding portable GPS unit, so they devise an alternative plan: The hapless intern is given a reflective survey marker and instructed to climb the mountain, positioning the marker at the peak. The rest of the team find a comfortable point on the beach at sea level, set up their precision inclinometer and laser rangefinder, and mix up some drinks while they wait for the intern to reach the peak. When he finally gets up there, they use the inclinometer to measure the angle of elevation from the beach position to the target at the peak and the laser rangefinder to measure straightline distance between the two points. The inclinometer indicates an angle of 28.73° to the peak, and the rangefinder measures a distance of 3475.4 meters. Draw a diagram, set up a formula with the relevant function, and find the height of the mountain in meters. Assume that the gear which wasn't damaged by the intern is highly accurate, disregard the minor influence of the curvature of the Earth, and round to the nearest tenth of a meter.

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