Find the Bearing from A to C & Angle B: Solve Here

In summary, the conversation involved finding the distance and bearing from point A to point C, given that an airplane had flown from point A to B with a bearing of 25 degrees and then from point B to C with a bearing of 40 degrees. The distance was found using the law of cosines and the angle BAC was found using either the sine or cosine law. The value of angle ABC was determined to be 165 degrees.
  • #1
cbarker1
Gold Member
MHB
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Dear everyone,

An airplane flies 470 miles from point $A$ to point $B$ with a bearing of 25 degrees. It then flies from 250 miles from point $B$ to point $C$ with a bearing of 40 degrees. Find the distance and the bearing from A to point C.
Work

Bearing Problem.png

I understand that I need to use law of cosines for the side $b$ which is opposite of the angle $B$. But I have a hard time with find what is the angle $B$ is. I forgot many things from geometry. How to determine the angle from point $A$ to point $C$?

Thanks
Cbarker1
 
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  • #2
$AC = \sqrt{470^2+250^2 - 2(470)(250)\cos(165)}$

bearing = $25^\circ + m\angle{BAC}$

$\angle{BAC}$ may be found using either the sine or cosine law
 
  • #3
How did you determine the angle ABC to be 165?
 
  • #4
bearings.jpg
 

1. What is the purpose of finding the bearing from A to C and angle B?

The purpose of finding the bearing from A to C and angle B is to determine the direction and angle between two points. This information is commonly used in navigation and surveying.

2. How do you calculate the bearing from A to C?

To calculate the bearing from A to C, you need to use the formula: bearing = atan2(y,x), where y is the difference in longitude and x is the difference in latitude between points A and C. The result will be in radians, which can be converted to degrees if needed.

3. What is the difference between bearing and angle?

Bearing and angle are both measurements of direction, but they are calculated differently. Bearing is the direction from one point to another, measured clockwise from north. Angle is the amount of rotation between two intersecting lines or planes.

4. How do you use the bearing and angle to solve for a missing side or angle?

If you have the bearing and angle between two points, you can use trigonometric functions (such as sine, cosine, and tangent) to solve for a missing side or angle in a triangle. You will need to know at least one side and one angle to use these functions.

5. Can the bearing from A to C and angle B be negative?

Yes, the bearing from A to C and angle B can be negative. This indicates a direction or angle in the opposite direction from the positive value. For example, a bearing of -45 degrees means that the direction is 45 degrees west of north.

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