trigonometry HARD!!
posted by jake on .
An airplane flies due north from a starting point at 234.6 mph for 40 minutes. Then turns flying 20 minutes at 252 mph in the direction N 20 degree 31 minutes East. How many miles is the airplane from the starting point?

find the two distances:
northbound part = 234.6(40/60) = 156.4 miles
NE part = 252(20/60) = 84 miles
N 20°31' E = N 20.5166667 ° E
I see a triangle with sides 156.4 and 84 with an angle of 159.48333 between them.
by cosine law
x^2 = 156.4^2 + 84^2  2(156.4)(84)cos 159.48333
= ...
I will let you slug it out
(I got 236.9 miles)