SOLUTION: a mine shaft goes straight down for 110m. from its lower end a horizontal tunnel goes 35m east and then 70m south to its end.what is the displacement from the top of the shaft to t
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Question 91857: a mine shaft goes straight down for 110m. from its lower end a horizontal tunnel goes 35m east and then 70m south to its end.what is the displacement from the top of the shaft to the end of the tunnel?what angle does this displacement make with respect to the vertical line? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! a mine shaft goes straight down for 110m. from its lower end a horizontal tunnel goes 35m east and then 70m south to its end.what is the displacement from the top of the shaft to the end of the tunnel?what angle does this displacement make with respect to the vertical line?
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I would think of this as a rectangular box, dimensions of 110 by 35 by 70.
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The displacement from the top to the given point would be the diagonal from
one corner of the box to the opposite corner.
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This length would be the hypotenuse (h) of a triangle formed by 110 m line and the diagonal of the base which is 35 by 70.
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Find the diagonal of the base (bd)
base diag = Sqrt(35^2 + 70^2)
base diag = 78.262379 m
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Find h:
h = Sqrt(110^2 + 78.26379^2)
h = 135 m is the displacement from the top of the shaft to the given point
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Angle (A) from the vertical can be found by using the Cosine
Cos(A) = 110/135
A = 35.43 degrees is the angle from the vertical
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Did this make sense? I hope so. Let me know if I screwed this one up.
