CK-12-Pre-Calculus Concepts

7.3. Resolution of Vectors into Components http://www.ck12.org

(

305 √ 3

2

) 2

+

( 395

2

) 2

=c^2

329. 8 ≈c

The airplane is traveling at about 329.8 mph.
Since you know thexandycomponents, you can use tangent to find the angle. Then convert this angle into bearing.

tanθ=

( 395

2

)

( 305 √ 3

2

)

θ≈ 36. 8 ◦

An angle of 36. 8 ◦on the unit circle is equivalent to a bearing of 53. 2 ◦.
Note that you can do the entire problem in bearing by just switching sine and cosine, but it is best to truly understand
what you are doing every step of the way and this will probably involve always going back to the unit circle.
Concept Problem Revisited
Consider four siblings fighting over a candy in a four way tug of war. Lanie pulls with 8 lb of force at an angle
of 41◦. Connie pulls with 10 lb of force at an angle of 100◦. Cynthia pulls with 12 lb of force at an angle of
200 ◦. How much force and in what direction does poor little Terry have to pull the candy so it doesn’t move?

To add the three vectors together would require several iterations of the Law of Cosines. Instead, write each vector
in component form and set equal to a zero vector indicating that the candy does not move.