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

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?
:
I would think of this as a rectangular box, dimensions of 110 by 35 by 70.
:
The displacement from the top to the given point would be the diagonal from
one corner of the box to the opposite corner.
:
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.
:
Find the diagonal of the base (bd)
base diag = Sqrt(35^2 + 70^2)
base diag = 78.262379 m
:
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
:
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
:
Did this make sense? I hope so. Let me know if I screwed this one up.

RELATED QUESTIONS
Hi :o) I hope you guys can help me with this. I think I now understand how to work out a (answered by stanbon)

A plane flies 8 miles south from the airport then 15 miles east. It then goes in a... (answered by stanbon)

A car drives south at 20 mi.per hr. Another car, starting from the same point at the... (answered by ikleyn)

A car goes 24miles due north then 7miles due east .What is the straight distance between... (answered by ikleyn)

A man travels 7 miles due north, then goes 3 miles east and then 4 miles south. How far... (answered by rfer)

A hiker goes six miles east and then turns south. If the hiker finishes 7.2 miles from... (answered by richwmiller,stanbon)

adam travels 35 miles west and then 42 miles south. how far away is he from his starting... (answered by Alan3354,josgarithmetic)

Solve. Use a graphing calculator if necessary. See Examples 9 - 11. (Objective 8) From (answered by ikleyn)

From the top of the building, a ball is thrown straight up with an initial velocity of... (answered by Solver92311,ikleyn)