SOLUTION: A ramp at the loading dock of an automobile mnufacturing plant makes a 13 degree angle with the ground. The bottom of the ramp is 25 m from the building. What is the length of th

Question 458783: A ramp at the loading dock of an automobile mnufacturing plant makes a 13 degree angle with the ground. The bottom of the ramp is 25 m from the building. What is the length of the ramp to the nearest meter?
I tried cos 13=25/x but it gives me about 25.8. According to the answer key, the answer is 24. What am I doing wrong??
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Check to make sure that you have copied the problem correctly.
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From the way you have written the problem and described your method of solving it, you have done nothing wrong.
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Examine the problem logically. The ramp is the hypotenuse of a right triangle in which the distance from the base of the ramp to the building is one leg and the distance from the ground to the high end of the ramp is the other. Since the ramp is the hypotenuse of this triangle, by the properties of right triangles it must be longer than either of two legs. This means that the length of the ramp cannot be shorter than than the 25 meters of the one given leg. Therefore, the ramp cannot be 24 meters.
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Your setup of the problem was correct:
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in which 25 is the adjacent side of the angle and x is the length of the ramp or the hypotenuse.
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A quick way of looking at the next step is just to swap the positions of the x and the cos(13) in this function so that the equation becomes:
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If you have a "normal" scientific calculator, you can solve for x by entering 25, pressing the divide key, entering 13 (presuming you are in the degree mode and not the radian mode), pressing the cos key, and finally pressing the = key.
When you do that, you should get the length of the ramp to be 25.65760269 meters which rounds to 25.7 meters.
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So, if you have stated the problem correctly (including all the dimensions), and you are looking at the right number in the answer key, then the only option remaining is that the answer key is wrong. Don't you just hate it when they do that? It sure causes a lot of extra work and worry, doesn't it? You understand what you are doing and how to use the cosine function to solve problems, and that's the most important part!
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