How to Solve a Trigonometry Word Problem Involving Distances

  • #1
nmnna
22
3
Homework Statement
A map shows a straight road crossing two contour levels 100ft., 200ft. at P, Q. The length of PQ is 1.2 inches, and the scale of the map is 4 inches to the mile. What average angle does the road make with the horizontal?
Relevant Equations
The sketch:
1616055720828.png

First of all find the length of PQ on i.e




Now, I do not understand where shall I draw the horizontal, and the connection between the lengths of the contours, so I'll be grateful if you give me some hints for solving this problem.
Thank you.
 
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  • #2
Why don't you draw the road incline from the side?
 
  • #3
PeroK said:
Why don't you draw the road incline from the side?
1616059506536.png

Like this?
 
  • #4
No. From the side. So you can see the road going uphill!
 
  • #5
PeroK said:
No. From the side. So you can see the road going uphill!
You mean from the opposite side? Sorry for my dumbness..
 
  • #6
A map is a "Plan". You want an "End Elevation" or "Side Elevation":

 
  • #7
PeroK said:
A map is a "Plan". You want an "End Elevation" or "Side Elevation":


I think I understand now.
So the difference between the heights of the road is 100, I have the length of PQ, what I need to do now is to calculate the angle, right?
 
  • #8
nmnna said:
I think I understand now.
So the difference between the heights of the road is 100, I have the length of PQ, what I need to do now is to calculate the angle, right?
Note that the distances on a map (you should be able to find out this sort of thing yourself from the Internet) are horizontal distances, not the hypoteneuse of slopes.
 
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  • #9
PeroK said:
Note that the distances on a map (you should be able to find out this sort of thing yourself from the Internet) are horizontal distances, not the hypoteneuse of slopes.
Okey, sorry for the trouble
 
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