Physics Help Forum Vectors and angles

 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum

 Jan 20th 2010, 08:05 PM #1 Junior Member   Join Date: Jan 2010 Posts: 22 Vectors and angles The treasure map in the figure gives the following directions to the buried treasure: "Start at the old oak tree, walk due north for 490 paces, then due east for 130 paces. Dig." But when you arrive, you find an angry dragon just north of the tree. To avoid the dragon, you set off along the yellow brick road at an angle east of north. After walking 330 paces you see an opening through the woods. Which direction should you go to reach the treasure? (in degrees west of north)???? I first found the hypotenuse of the first right triangle with the sides 490 and 130. This was found to be 507. The angle opposite of the 130 (where the starting point is) was found to be 14.9 degrees. I then drew a new triangle with sides 507, 330, and c. c is across from the 45.1 degree angle (60 - 14.9 = 45.1). i used law of cosine to solve for c and found that to be 360.2 i then used law of sine to find the angle across from 507. This was found to be 85.6 degrees. i found that the angle west of north was 49.3 degrees but this was incorrect? Could i get some help with this please. Thank you Last edited by mybrohshi5; Jan 20th 2010 at 08:16 PM.
Jan 21st 2010, 07:57 AM   #2
Member

Join Date: Jan 2010
Posts: 48

Hi

first of all, please see the attached file. here is a figure to draw your situation (please forgive for rough diagram since I am not a better user of graphic software)

Here AB = 490, AF = 130, BC = 330 (equivalent to as given by your statement)

find angle ABF (shown in red) using simple trignometry which comes out to be 14.9 degree (you have already calculated it) and calculate BF using Pythagorus theorem which comes out to be 506.9. Now angle FBD becomes 60-14.9 = 45.1 degree.

Now BD = BF cos 45.1 = 357.8 and DF = BF sin 45.1 = 359.1

Now CD = BD-BC = 357.8-330 = 27.8

using these CD and FD you can calculate angle FCD which comes out to be 85.57 degree. since you want answer as west of north so just subtract 60 from 85.57 and answer become 25.57 degree.

please confirm whether I am right or not!!!
Attached Images
 problem.bmp (576.1 KB, 277 views)

Last edited by vyomictor; Jan 21st 2010 at 08:33 AM. Reason: change in figure

 Jan 21st 2010, 08:11 AM #3 Junior Member   Join Date: Jan 2010 Posts: 22 That is correct. So i had all the right stuff sorta just couldnt get the right angle. Could you please explain why you had the extra FCD triangle in there and why you subtracted 85.6 - 60 to get the angle of west of north???? i just am having trouble comprehending the last part of this thing i guess. any further explanation would be much appreciated and thanked.
 Jan 21st 2010, 08:35 AM #4 Member   Join Date: Jan 2010 Posts: 48 reply please refer to figure again, I have just introduced a new point G. Now AB and CG are parallel so I just have subtracted 60 from 85.57 and the green part corresponds to this extra. any other query will be welcomed!!!
 Jan 21st 2010, 08:48 AM #5 Junior Member   Join Date: Jan 2010 Posts: 22 for some reason i cannot just picture what is going on and where the subtraction of 60 comes in from Thank you for the help though
 Jan 22nd 2010, 07:58 AM #6 Member   Join Date: Jan 2010 Posts: 48 reply Hi, dear it is very clear. You can look into the figure can visualize the situation that angle FCD is greater than 60 degree. If answer is asked in the form of angle with respect to direction BE then result will be only 85.57 degree. since answer is asked in respect to the north direction so i just subtracted 60. Now there is final attempt from my side. Look into the figure! lines AB (given) and CG (constructed by us in north direction to calculate result) both lie in north direction. since both are in same direction so must be parallel. Now due to this angle ABC would be equal to angle GCD (corresponding angles). now to calculate angle FCG (which is our result) the process is angle FCG = angle FCD-angle GCD. I hope it is clear now best wishes!!!!! bye
 Jan 22nd 2010, 08:01 AM #7 Junior Member   Join Date: Jan 2010 Posts: 22 you way is clear i just did it a different way and cannot figure out how to get the right angle with the way i solved it. its ok though. thank you for you time and explanations. they were very helpful.

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