Chapter 7 review

Number 73

This method shows how to find the direction by adding the vector.You will use the laws of sines and cosines.

To view this show, right click on screen and select “full screen”.

Draw the picture

80o

310o

Place the vectors so that they have the same starting point.

80o

Find the angle between the vectors.

80o

40o

10o

40 + 10 = 50o

Draw a parallelogram.

80o

40o

10o

Let’s make the picture bigger and find all the angles.

50o

50o

The sum of the angles is 360o.

360 – 50 – 50 2

= 130o

130o

130oRemember:Opposite angle are equal.

Label the sides and draw the resultant.

50o

50o

130o

20

160

20

160

R

130o

Remember:Opposite sides are equal.

Notice that the resultant creates two triangles

Let’s look at one triangle and use the law of cosines to find the length of the

resultant.

130o

160

20

R

r2 = 1602 + 202 – 2(160)(20) cos 130o

r = 174

c2 = a2 + b2 – 2ab cos

r = the length of the resultant.

Find the drift angle.

130o

160

20

R

20sin x

174sin 130o

r = 174

x

=

x = 5o

The plane is off course by 5o.

Therefore it is traveling at a direction of 85o.