How Do You Calculate Distances and Angles for Multiple Treasure Map Routes?

[XPX1]

A treasure map directs you to start at a palm tree and walk due north for 12.0 m. You are then to turn 90° and walk 13.0 m; then turn 90° again and walk 5.00 m. For each of the four possible locations of the treasure, give the distance from the palm tree and the direction, expressed as an angle measured counterclockwise from north. List the possible locations in counterclockwise (CCW) order, starting with the one which is closest to due east.
14.76m and ° (location which is farthest east)
_____m and ° (next location in the CCW direction)
_____m and ° (next location in the CCW direction)
_____m and ° (next location in the CCW direction)


Hello, I am completely lost with this question, here is the steps I did to get the first answer, 14.76m with is correct.


I am supposed to walk north 12m, y = 12, then I turn 90 degrees and walk right for 13m x = 13 then I turn 90 degrees and walk back down 5m. So y = 12-5=7 because I walked up 12m and then back down 5 meters and x = 13.

Knowing this I can construct a triangle
x=13
_____
y=7 | /
| /
|_/

a^2+b^2=C^2

13^2+7^2 = 218

Square root of 218 is 14.764, so the answer to the first question is 14.764, but how do I figure out the degrees for it counterclockwise, and find the rest of the answers for the problem? I tried setting x negative since I could walk left, but that did not give me a correct answer for one of them, please help!

 

[alfredbester]

Your overcomplicating things, I assume the treasure is located at each point turning point. The first treasure point (third on your list) is the easiest it's located at 12m and 0°, when it says turn 90° your are turning on a right angle to your right.

 

[XPX1]

12m and 0 degrees was wrong :( I still don't quite understand

 

[Max Eilerson]

Palm tree has the co-ordinate (0m,0m)
1) you travel 12m North new co-ordinate (12m,0m)
2) turn 90° (due east) you walk 13m new co-ordinate (12m, 13m)
3)turn 90° (due south) you walk 5m new co-ordinates (7m,13m).

You have worked out the distance correctly, do you know the trigonometric relations?

 

[XPX1]

Not really, all I know is that I am confused, and I know what Sin Cos Tan and Tan -1 do

 

[Max Eilerson]

$$tan /theta = x/y$$

 

[XPX1]

Im still lost. I know how to do the first part for meters, but I do not know how to get the degrees, or anything else, and none of this stuff above is making sense?

tan/Theta = x/y? what does that give me though? does it tell me how many meters I am supposed to go to get the treasure? or the degrees needed for the answer? both? I am confused.

 

[XPX1]

Can someone please tell me how to get the answers for the questions above just plain and simple, all this other stuff doesn't seem to fit into the problem I am being asked. Its not asking about where I am at in just meters, its asking where I am at in meters and next location in degrees in the counterclockwise direction

 

[XPX1]

bump for great justice

 

[HallsofIvy]

A treasure map directs you to start at a palm tree and walk due north for 12.0 m. You are then to turn 90° and walk 13.0 m; then turn 90° again and walk 5.00 m. For each of the four possible locations of the treasure, give the distance from the palm tree and the direction, expressed as an angle measured counterclockwise from north. List the possible locations in counterclockwise (CCW) order, starting with the one which is closest to due east.
14.76m and ° (location which is farthest east)
_____m and ° (next location in the CCW direction)
_____m and ° (next location in the CCW direction)
_____m and ° (next location in the CCW direction)

I assume the "possible locations" is because you aren't told whether you turn left or right at each point. You turn twice and since at each turn you have 2 choices: right or left- so there are 2(2)= 4 possible answers.
Don't use triangles or trigonometry until after you have found the final position- just keep the N-S and E-W distances separate. I'm going to use + for N or E, - for S or W:
Assuming you turn right both times:
First walk 12 m N: NS 12 EW 0
turn right walk 13 m E: NS 12 EW 13
turn right walk 5 m S: NS 12- 5= 7 EW 13
From your original position you know have a right triangle with legs of length 7 and 13 m. Use the Pythagorean theorem to find the length of the hypotenuse (distance from original point to final point) and use
tan$\theta$= 7/13 to find the angle.

Turn right first time but left second time:
First walk 12 m N: NS 12 EW 0
turn right walk 13 m E: NS 12 EW 13
turn left walk 5 m N: NS 12+ 5= 17 EW 13
You now have a right triangle with legs of length 17 and 13. Again use the Pythagorean theorem to find the distance, tan$\theta$= 17/13 to find the angle.

Turn left first time, right second time
First walk 12 m N: NS 12 EW 0
turn left walk 13 m W: NS 12 EW -13
turn right walk 5 m S: NS 12- 5= 7 EW -13
You again have legs of length 7 and 13 (length is always positive) so the same distance as before but now tan$\theta$= -7/13.

Turn left both times
First walk 12 m N: NS 12 EW 0
turn left walk 13 m W: NS 12 EW -13
turn left walk 5 m N: NS 12+ 5= 17 EW -13
Now you have a right triangle with legs of length 17 and -13 so the same distance as before but the angle is given by tan$\theta$= -17/13.