Posted by Adrianna on .
Two airplanes take off from an airport at the same time. One travels on a heading of 45 at 420 mph and the other on a heading of 150 at 400 mph. After two hours, how far apart are the airplanes?
A.650.66 miles
B.1,160 miles
C.1,301 miles

PreCal 
Reiny,
Use the cosine law, I got 650.66

PreCal 
Adrianna,
Can you tell me how you did it? I got 5 more questions like this one.

PreCal 
Reiny,
are you not familar with the cosine law?
You must have learned this to be able to do this kind of question. 
PreCal 
Adrianna,
Yes I am, but I don't understand it. I don't have a teacher to teach me. I do my work online, and I just need 2nd semester of precal to graduate.

PreCal 
Reiny,
x^2 = 420^2 + 400^2  2(420)(400)cos 105°
do the arithmetic
I got 105° from the difference between 150° and 45° 
PreCal 
Adrianna,
thanks

PreCal 
Henry,
d1 = 420mi/h[45o] * 2h = 840mi[45o]
d2 = 400mi/h[150o] * 2h = 800mi[150o]
D = 840[45o]  800[150o]
X = 840*Cos45  800*cos150 = 1287 mi
Y = 840*sin45  800*sin150 = 194 mi
D = sqrt(1287^2+194^2) = 1301.5 mi