An airplane flies 165 miles from point A in the direction 130 degrees and then travels in the direction 245 degrees for 80 miles. Approximately how far is the airplane from A?

Answer 1

the first leg moves the plane in th x- and y-directions by

(165*cos40°,-165*sin40°)

Now figure the amounts of the second leg, add them up, and then use the distance formula.

Answer 2

The subject says algebra, but since you apparently have had some trig, just use the law of cosines:

x^2 = 165^2 + 245^2 - 2(165)(245)cos115°

Answer 3

I really don't know where Steve got his numbers from.

Making a sketch I have a triangle with sides 165 and 80 and an angle of 65° between them, so by the cosine law
x^2 = 80^2 + 165^2 - 2(80)(165)cos 65°
= 22467.87789
x = appr 149.9 miles

Using vectors we have
(165cos 30°, 165sin130°) + (80cos245°,80sin245°)
= ....
= (-139.869.. , 53.892..)
and the magnitude of that vector is 149.9 miles

check: the direction :
tanØ = 53.892/-39.869
= -.385...
Ø = 158.9 or appr 159° which was consisten with my diagram.