You and your team are exploring a river in South America when you come to the bottom of a tall waterfall. You estimate the cliff over which the water flows to be about 100 feet tall. You have to choose between climbing the cliff or backtracking and taking another route, but climbing the cliff would cut two hours off of your trip. There is only one experienced climber in the group: she would climb the cliff alone and drop a rope over the edge to lift supplies and allow the others to climb without packs. The climber estimates it will take her 45 minutes to get to the top. However, you are concerned that the rope might be too short to reach the bottom of the cliff (it is exactly 30.0 m long). If it is too short, she'll have to climb back down (another 45 minutes) and you will be too far behind schedule to get to your destination before dark. As you contemplate how to determine whether the rope is long enough, you notice that the late afternoon shadow of the cliff grows as the sun descends over its edge. You suddenly remember your trigonometry. You measure the length of the shadow from the base of the cliff to the shadow's edge (144 ft), and the angle subtended between the base and top of the cliff measured from the shadow's edge. The angle is 38.1°. Do you send the climber, or start backtracking to take another route
You and your team are exploring a river in South America when you come to the bottom of a tall waterfall. You estimate the cliff over which the water flows to be about 100 feet tall. You have to choose between climbing the cliff or backtracking and taking another route, but climbing the cliff would cut two hours off of your trip. There is only one experienced climber in the group: she would climb the cliff alone and drop a rope over the edge to lift supplies and allow the others to climb without packs. The climber estimates it will take her 45 minutes to get to the top. However, you are concerned that the rope might be too short to reach the bottom of the cliff (it is exactly 30.0 m long). If it is too short, she'll have to climb back down (another 45 minutes) and you will be too far behind schedule to get to your destination before dark. As you contemplate how to determine whether the rope is long enough, you notice that the late afternoon shadow of the cliff grows as the sun descends over its edge. You suddenly remember your trigonometry.
You measure the length of the shadow from the base of the cliff to the shadow's edge (144 ft), and the angle subtended between the base and top of the cliff measured from the shadow's edge. The angle is 38.1°. Do you send the climber, or start backtracking to take another route
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