A small map shows Pittsburgh to be 343 miles in a direction 23° north of east from Louisville. The same map shows that Detroit is 209 miles in a direction 48° west of north from Pittsburgh. Assume a flat earth and use the given information to find the displacement from Louisville to Detroit.
What is the magnitude and the direction?
2007-09-09 04:09:54 · 3 answers · asked by dazedandconfused 2 in Science & Mathematics ➔ Physics
Did you use the law of cosines? 109 degrees being the angle opposite of the distance between Louisville and Detroit (since 180-48-23= 109)? I got 141.89 miles between them.
2007-09-09 04:25:48 · answer #1 · answered by CTN 2 · 0⤊ 0⤋
X(horizontal distance):
x = 343cos23 - 209sin48
x = 160.416miles
Y(vertical distance):
y = 343sin23 + 209cos48
y = 273.869
Distance:
Dist. = √((160.416)^2 + (273.869)^2) = 317.39miles
Direction(angle):
Dir. = arctan(273.869/160.416) = 59.64 degrees north of east
-As freebe said, make sure your calculator is in degree mode.
-The angle CTN found, 109 degrees is not an angle of the triangle formed by the three locations.
- Draw the sketch carefully, and make sure you understand the above equations, if not resubmit.
2007-09-09 05:02:29 · answer #2 · answered by jsardi56 7 · 0⤊ 0⤋
Is your calculator in radian mode? Because that could be the problem.
2007-09-09 04:32:01 · answer #3 · answered by cmufreebie88 2 · 0⤊ 0⤋