SOLUTION: A tight rope walker wants to walk across the length of the Niagara Falls, and needs to determine the length of the wire needed to do this feat. The length across the falls is 790m.

Algebra ->  Trigonometry-basics -> SOLUTION: A tight rope walker wants to walk across the length of the Niagara Falls, and needs to determine the length of the wire needed to do this feat. The length across the falls is 790m.      Log On


   

Question 1187942: A tight rope walker wants to walk across the length of the Niagara Falls, and needs to determine the length of the wire needed to do this feat. The length across the falls is 790m. When the walker is halfway across the angle of depression of the wire is 18 degrees. How high above the water level should the wire be attached if the wire is to get no closer than 3.0m to the water.
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
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Make a sketch.  It will help you better understand my formulas.



The length of the rope can not be less than  2%2A%28790%2F2%29%2Fcos%2818%5Eo%29%29 = 790%2F0.9511 = 830.6 meters.      ANSWER


Here I calculated the length of the hypotenuse, using the length of the leg adjacent to the 18° angle.

 



The rope should be attached at least as high as  


    3+%2B+%28%28790%2F2%29%29%2Atan%2818%5Eo%29 = 3+%2B+395%2A0.3249 = 131.34 feet over the water surface.      ANSWER


Here I calculated the length of the opposite leg using the length of the leg adjacent to the  18° angle.

Solved.

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