Physics
posted by Anna .
A plane is capable of flying 200 km/h. There is a wind of 90 km/h from the east. The pilot flies in a northwest direction relative to the ground for three hours from city A to city B. Find the speed of the plane relative to the ground, the heading of the plane, and the distance between city A and city B.

Cosine Law
u=sqrt(V²+v²2•V•v•cos135°)=
=sqrt(200²+90²2•200•90•cos135°)=
=sqrt(40000+8100 +25455.8)=271 km/h
s=u•t=271•3=813 km
Sine Law
271/sin135°=90/sinβ
sinβ=90•sin135°/271=0.235
β=13.6° (northwest, respectively west direction)