SOLUTION: Two small planes leave the airport at the same time. The first flies at 225 km/h at a heading of 320°, while the second flies at 190km/h at a heading of 70°. How far apart are th

Algebra ->  Trigonometry-basics -> SOLUTION: Two small planes leave the airport at the same time. The first flies at 225 km/h at a heading of 320°, while the second flies at 190km/h at a heading of 70°. How far apart are th      Log On


   

Question 1161847: Two small planes leave the airport at the same time. The first flies at 225 km/h at a heading of 320°, while the second flies at 190km/h at a heading of 70°. How far apart are they after 2 hours?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two small planes leave the airport at the same time.
The first flies at 225 km/h at a heading of 320°,
while the second flies at 190km/h at a heading of 70°.
How far apart are they after 2 hours?
:
The first plane is 320 degrees which 40 degrees west of north
the second plane is 70 degrees east of north.
Therefore the angle between the two planes 40 + 70 = 110 degrees
:
The distance each has traveled
The first plane 2 * 225 = 450 km
The second plane 2 * 190 = 380 km
:
The law of cosines: a^2 = b^2 + c^2 -2bc Cos(A)
where
A = 110 degrees
a = distance between the planes after 2 hrs
b = 450
c = 380
:
a^2 = 450^2 + 380^2 - 2(450*380)*Cos(110)
a^2 = 202500 + 144400 - 2(171000)*-.342
a^2 = 346900 -(-116971)
a = sqrt%28463871%29
a = 681 km apart after 2 hrs
:
Some tedious math here, check it!