the angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 31 degrees. if the vertical distance from the bottom to the top of the mountain is 902 feet and the gondola moves at a speed of 155 feet per minute, how long does the ride last? round to the nearest minute

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I'm assuming that the ride covers the initial point, at which the angle of elevation € is 31°, to the end of the ride, which equals the bottom of the mountain. So if we set up a right triangle from the gondola to the bottom of the mountain, whuch becomes our ride distance (d), the height from that bottom to the mountain top (h), and the hypotenuse being the line of sight from the mountain top to the gondola. So the tan € = opposite / adjacent, where € is the angle of 31, opposite is the mountain height (h), which is 902 ft, and the bottom is ride distance (d), the distance that we're looking for. Now: tan 31 = h/d = 902/b --> b = 902/tan31 = 1501.18 ft We can now determine how long the ride is, since the distance = 1501 and the speed or rate given = 155 ft/min distance = rate(r) × time (t) --> d = r × t --> t = d ÷ r = 1501ft ÷ 155ft/min --> t = 9.685 minutes

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