A plane flies in a direction of 85° from Chicago. It then turns and flies in the direction of 200° for 150 miles. It is then 195 miles from its starting point. How far did the plane fly in the direction of 85°?

Question

A plane flies in a direction of 85° from Chicago. It then turns and flies in the direction of 200° for 150 miles. It is then 195 miles from its starting point. How far did the plane fly  in the direction of 85°?

I am confused about aereal navigation. Can someone help me?

Reiny · Answer

I made a sketch with Chicago as C, A as the end of the first flight, and B as the end of the 2nd flight.
In triangle ABC
AC = x, AB = 150, BC = 195, angle A = 65°
by the sine law:
sinC/150 = sin 65/195
sinC = .69715...
C = 44.199... (I stored that in calculator's memory)
then angle B = 180 - 65 - 11.199.. = 70.8004...
again, by the sine law,
x/sin70.8004.. = 195/sin65
x = 203.19 miles

Danny · Answer

Thank you a lot you saved my life.

Jillian · Answer

I don't understand where do you get the 65 from?