SOLUTION: two people walk away from each other at an angle, one moving straight ahead at left 6 feet per second, the other is moving straight ahead at 4 feet per second. After 5 seconds, the

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Question 390225: two people walk away from each other at an angle, one moving straight ahead at left 6 feet per second, the other is moving straight ahead at 4 feet per second. After 5 seconds, they are 45 feet apart. If they continue the same angle, How far apart will be after one minute.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
two people walk away from each other at an angle, one moving straight ahead at left 6 feet per second,
the other is moving straight ahead at 4 feet per second. After 5 seconds, they are 45 feet apart.
If they continue the same angle, How far apart will be after one minute.
:
Find out how far each has gone in 5 sec
1: 6 * 5 = 30 ft
2: 4 * 5 = 20 ft
At this time they are 45 ft apart,
a triangle:
a = 30
b = 20
c = 45
We want to find angle C. (opposite 45'); use the law of cosines
c^2 = a^2 + b^2 - 2bc *cos(C)
:
Rearrange to find C
2bc*cos(C) = a^2 + b^2 - c^2
:
2(30*20)cos(C) = 900 + 400 - 2025
1200cos(c) = -725
cos(C) = %28-725%29%2F1200
cos(C) = -.604
C = 127.157 degrees
:
Find the distance walked in 1 min
a: 6 * 60 = 360'
b: 4 * 60 = 240'
c: dist apart after 1 min
:
Use the law of cos again
c^2 = a^2 + b^2 - 2bc *cos(C)
c^2 = 360^2 + 240^2 - 2(360*240)cos(127.157)
c^2 = 129600 + 57600 - 2(86400)*-.604
c^2 = 187200 - (-104371)
c^2 = 291571
c = sqrt%28291571%29
c ~ 540' apart after 1 min
:
Please let me know if screwed this one up. Carl