Thread: Bearings Problem - driving me nuts!!

1. Bearings Problem - driving me nuts!!

Plane A flies a distance of 220 miles in the direction N20(degrees)E.
Plane B departs from the same airport and flies a distance of 365 miles in the direction S55(degrees)W.

Calculate the distance between the two planes.

Any help would be much appreciated!!!
Thank you!!

2. Originally Posted by Shmomo89
Plane A flies a distance of 220 miles in the direction N20(degrees)E.
Plane B departs from the same airport and flies a distance of 365 miles in the direction S55(degrees)W.

Calculate the distance between the two planes.

Any help would be much appreciated!!!
Thank you!!
Use cosine theorem

3. Hello, Shmomo89!

repcvt gave you an excellent game plan . . .

Plane $\displaystyle A$ flies a distance of 220 miles in the direction N20°E.
Plane $\displaystyle B$ flies a distance of 365 miles from the same airport in the direction S55°W.

Calculate the distance between the two planes.
Code:
                            |
|           o A
|         **
|       * *
|     *  *
|   *   *
| *    *
*     * 220
* |    *
*   |20°*
*     |  *
*       | *
*         |*
- - - - - - - * - - - - - o - - - - - - - -
*         *55°|O
*       *       |
*     * 365       |
*   *               |
B o                     |

We find that $\displaystyle \angle AOB = 145^o$

Now use the Law of Cosines on $\displaystyle \Delta AOB.$

. . .$\displaystyle AB^2 \;=\;365^2 + 220^2 - 2(365)(220)\cos145^o$ . . . etc.