1. 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”.

2. Draw the picture 80 o 310 o

3. Place the vectors so that they have the same starting point. 80 o

4. Find the angle between the vectors. 80 o 40 o 10 o 40 + 10 = 50 o

5. Draw a parallelogram. 80 o 40 o 10 o

6. Let’s make the picture bigger and find all the angles. 50 o The sum of the angles is 360 o. 360 – 50 – 50 2 = 130 o 130 o Remember: Opposite angle are equal.

7. Label the sides and draw the resultant. 50 o 130 o 20 160 20 160 R 130 o Remember: Opposite sides are equal. Notice that the resultant creates two triangles

8. Let’s look at one triangle and use the law of cosines to find the length of the resultant. 130 o 160 20 R r 2 = 160 2 + 20 2 – 2(160)(20) cos 130 o r = 174 c 2 = a 2 + b 2 – 2ab cos  r = the length of the resultant.

9. Find the drift angle. 130 o 160 20 R sin x 174 sin 130 o r = 174 x = x = 5 o The plane is off course by 5 o. Therefore it is traveling at a direction of 85 o.