A girl walks at a distance of 2km and on a bearing of 107° at a point A to B,she changes direction from B to C,on a bearing of 017° and at a distance of 3km,what is the bearing from C to A?
A girl walks at a distance of 2km and on a HEADING of 107° at a point A to B,she changes direction from B to C,on a HEADING of 017° and at a distance of 3km,what is the bearing (YES, finally, ,, math books do not do navigation) from C to A?
anyway
107 = 17 deg below +x axis
17 = 17 degrees clockwise from +y axis (NOTE PERPENDICULAR to AB)
So ABC is a right triangle with 90 deg angle at B
so what is angle BAC ???
Tan BAC = 3/2 = 1.5
So BAC = 56.3 deg
so
AC = 56.3 - 17 = 39.3 deg above +x axis
so
Line AC is 90-39.3 = 50.6 deg clockwise from north
so
CA = AC + 180 = 230.6 deg clockwise from north
To find the bearing from point C to point A, we can use trigonometry and the concept of bearings.
Step 1: Draw a diagram:
Draw a diagram with three points, A, B, and C, with point A to the left, point B to the right, and point C above point B. Label the distances given in the problem.
Step 2: Determine the bearing from point B to A:
The bearing from B to A is 180 degrees less the given bearing from A to B, which is 107°. So the bearing from B to A is 180° - 107° = 73°.
Step 3: Determine the bearing from point C to A:
To find the bearing from C to A, we need to use the bearing from B to A and the bearing from C to B.
The bearing from C to B is 180° - the given bearing from B to C, which is 017°. So the bearing from C to B is 180° - 17° = 163°.
To find the bearing from C to A, we add the bearings from C to B and from B to A:
Bearing from C to A = Bearing from C to B + Bearing from B to A
Bearing from C to A = 163° + 73° = 236°.
Therefore, the bearing from point C to point A is 236°.
To find the bearing from point C to point A, we can use the concept of bearing angles. The bearing angle represents the angle between the direction of a straight line (usually a line of sight) and a reference direction, usually the north direction.
First, let's visualize the given information. We have three points: A, B, and C. Point A is the starting point, B is the intermediate point, and C is the final point.
Let's convert the given bearings to the standard compass bearing format (0° to 360°):
$\bullet$ The bearing from A to B is 107°.
$\bullet$ The bearing from B to C is 017°.
Now, let's find the bearing from C to A. We can obtain this by subtracting the bearing angle from A to B from 180°, and then adding the bearing angle from B to C.
Step 1: Subtract the bearing angle from A to B from 180°.
180° - 107° = 73°
Step 2: Add the bearing angle from B to C.
73° + 17° = 90°
Therefore, the bearing from C to A is 90°.
In summary:
The bearing from C to A is 90°.