Hey...so im having trouble with this question.....cant seem to figure it out:

The radar screen of an airport control tower shows that two planes are at the same altitude. According to the range finder, one plane is 100 km away, in the direction N60°E. The other is 160 km away, at a direction of S50°E. How far apart are the planes?

can i have some help?

3 answers

Draw a diagram, and review the law of cosines. The distance can be found via
d^2 = 100^2 + 160^2 - 2*100*160 cos70°
d = 157 km
Thanks for your help!
d = 100[60+180]+160[130o]
d = (100*sin240+160*sin130)+(100*cos240+160*cos130)i
d = 36-153i.
d = sqrt(36^2+153^2) = 157 km.