Question

A car travels 32 km due north and

then 46 km in a direction 40° west of
north. Find the DIRECTION of the car's
resultant vector.

Answer 1

Ifa,bandcare the

sides opposite to anglesA,B,&C.

By Cosine Rule,

b

2

=32

2

+46

2

−(2×32×46cos140°)

b

2

=1024+2116−2944cos140°

b

2

=3140−2944cos140°

b

2

=3140+2255.234841

b

2

=5395.234841

b=73.45

By Sine Rule,

sinC

32

​

=

sin140°

73.45

​

sinC=

73.45

32sin140°

​

sinC=0.2800

C=16.26°

The direction of the resultant

vector is measured from0°east

to the resultant, this angle isθ−90°,

90°is the total angle in

the first quadrant.

∴θ−90°=C+ϕ

ϕ=50°{Alternate angles are equal}

∴The direction of the car’s

resultant vector is50°+16.26°=66.26°south of east

Explanation: