Question 460692: A plane travels 160 miles at a heading of N 33 degrees W. It then changes direction and travels 205 miles at a heading of N 49 degrees W. How far is the plane from it's original position?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A plane travels 160 miles at a heading of N 33 degrees W. It then changes direction and travels 205 miles at a heading of N 49 degrees W. How far is the plane from it's original position?
..
I don't have the means to draw a diagram which would be the best way to show you how to solve given problem so I will give it a try with words.
..
If you draw the given headings correctly you should get a triangle with sides of 205 and 160 and their included angle of 164º. The problem can then be solved with the Law of Cosines.
let me describe what the diagram should look like:
Starting from a point labeled A, travel a distance of 160 miles rotated 33º west of North. At the end of the 160 miles, labeled point B, travel a distance of 205 miles rotated 49º west of North at point B. Mark the end of 205 miles as point C. Connect point C to beginning point A to complete the triangle. You now have a triangle with sides 160 & 205 with their included angle CBA. You can notice that this obtuse angle is made up of the complement of 49º=41º, the parallel angle of 33º plus 90º for a total of 41+33+90=164º
solution: Using Law of Cosines: c^2=a^2+b^2-2abCosC
let x= side CA
x^2=120^2+205^2-2*160*205*cos164º
x^2=14400+42025+63059=119484
x=346 miles
ans:
The plane is 346 miles from its original position
|
|
|
