An aeroplane flew 500 km south, then 600 km east. Give its true bearing from its starting point to the nearest degree.

Solution:

The vector diagram for various velocities is shown.Vector AC gives velocity of aeroplane relative to quiet air.Vector CB gives velocity of wind(air) relative to ground.Vector AB gives velocity of plane relative to ground.Using law of sines for triangle,

sin30

0

150

=

sinθ

20

.

Therefore,sin(θ)=

300

20

=

15

1

. Then,

Theta=sin

−1

15

1

=3.8

0

.

Angle NAC=33.8

0

.The pilot should head the plane in the direction 33.8

0

east of north

Step-by-step explanation:

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