Solving net horizontal word problem

dramaqueen
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the pathway for a mineshaft is described as follows: The first shaft extends north and down at an angle of 3.5 degree for 225ft to a vertical shaft which 125ft long. A third shaft then extends north and down at an angle 6.8 degree for 175ft. What is the total depth below ground level at the end of the third shaft? Also, what is the net horizontal distance from the ground opening to the end of the third shaft?

I look all over the chapter example and could figure out how to do it...

HELP!
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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