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In a sightseeing boat near the base of the Horseshoe Falls at Niagara Falls, a passenger estimates the angle of elevation to the top of the falls to be $30^{\circ} .$ If the Horseshoe Falls are 173 feet high, what is the distance from the boat to the base of the falls?
299.6 $\mathrm{feet}$
Precalculus
Algebra
Chapter 13
Trigonometric Functions
Section 1
Right Triangle Trigonometry
Trigonometry
An Introduction to Geometry
Introduction to Trigonometry
Campbell University
Oregon State University
McMaster University
University of Michigan - Ann Arbor
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hi, everyone. So today's problems says in a sightseeing boat near the base of the Horseshoe Falls at Niagara Falls. And passenger estimates that the angle of elevation to the top of the falls of the top of the falls to be 30 degrees. If the horse shit falls are 173 feet high. What is it? Visits from the boat to the base of the falls. Well, we can draw the waterfall right here, Okay, and says it is 100 and 73 feet high. Here is the distance, too. The boat in the here's well, and they said that the angle of elevation is about 30 degrees, so we can do tangent of 30 because the opposite over adjacent, he moves 173 over X. A little shortcut is we can just switch of both of these because if we multiply by X on both sides, we're gonna have to divide out tan or 30 on each side. So it'll still give us 173 over a tan of 30. So put on your calculator 173 divided by 10 of 30 and put your clothes in parentheses. E This gives us 200 99.64 for set your feet. Well, we're gonna run it to the nearest 10th. So the distance from the base of the waterfall to the boat is about 299.6 feet.
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