# Thread: Bearing Problems

1. ## Bearing Problems

For some reason I am having a terrible time with some bearing problems that were assigned. Any help would be greatly appreciated.
1. An airplane flew 450mi at a bearing of N65*E from Airport A to Airport B. The plane then flew at a bearing of S38*E to airport C. Find the distance from A to C if the bearing from airport A to Airport C is S60*E *=degrees
I can't get my angles to work out I know to use the law of sines, but I'm getting the wrong angles?

2. The Sides of a parallelogram are 10 feet and 14 feet. The longer diagonal is 18 feet. Find the length of the shorter diagonal of the parallelogram.
I don't understand how the shorter diagonal would look? |\| but wouldn't the shorter diagonal just make it look like an x inside of a box?

3. The heading and air speed of an airplane are 60* and 250 mph, respectively. If the wind is 50 mph with a direction of 150*, find the ground speed and resulting course (direction) of the plane.
I have no idea where to start this problem?

2. Originally Posted by jasonk
For some reason I am having a terrible time with some bearing problems that were assigned. Any help would be greatly appreciated.
1. An airplane flew 450mi at a bearing of N65*E from Airport A to Airport B. The plane then flew at a bearing of S38*E to airport C. Find the distance from A to C if the bearing from airport A to Airport C is S60*E *=degrees
I can't get my angles to work out I know to use the law of sines, but I'm getting the wrong angles?

...
Make a sketch. Calculate the angles and then use Sine rule.

3. Originally Posted by jasonk
...

2. The Sides of a parallelogram are 10 feet and 14 feet. The longer diagonal is 18 feet. Find the length of the shorter diagonal of the parallelogram.
I don't understand how the shorter diagonal would look? |\| but wouldn't the shorter diagonal just make it look like an x inside of a box?

...
1. Use the Cosine rule to calculate the magnitude of the angle $\phi$

2. Since $|\theta| = 180^\circ - |\phi|$ you can use the Cosine rule to calculate the length of the smaller diagonal.

4. Hello, jasonk!

You can start by making a sketch . . .

3. The heading and air speed of an airplane are 60° and 250 mph, respectively.
The wind is 50 mph with a direction of 150°.
Find the ground speed and resulting course (direction) of the plane.
Code:
      P                 Q
:                 :
:                 : 150°
:               B o
:               * : * 50
:             *60°:30°*
:      250  *     :     o C
:         *       : *
:       *       * :
:     *     *     :
:60°*   *         R
: * *
A o

The plane's heading is: $\angle PAB = 60^o,\;AB = 250$

The wind's heading is: $\angle QBC = 150^o,\;BC = 50$

Note that $\angle ABC = 90^o$

Then $AC$ is the hypotenuse of right triangle $ABC.$
. . $AC \:=\:\sqrt{250^2 + 50^2} \:=\:\sqrt{65,\!000} \;\approx\;255$

In right triangle $ABC\!:\;\;\tan(\angle BAC) \:=\:\frac{50}{250}\:=\:0.2$

. . then: . $\angle BAC \:=\:\arctan(0.2) \;\approx\;11.3^o$

Hence: . $\angle PAC \:=\:60^o + 11.3^o \:=\:71.3^o$

Therefore, the plane's heading is 71.3° and its speed is 255 mph.