A man starts from a Point a and walks 4km on a bearing of 015 to point b. He then walks 6km on a bearing of 105 to c. What is the bearing of c from a
If A is at (0,0) then
B is at (4 sin15°, 4 cos15°)
C is at B + (6 cos15°, -6 sin15°) =
(x,y) = (4 sin15° + 6 cos15° , 4 cos15° - 6 sin15°)
So the bearing of C from A is θ, where 90-θ where
tanθ = y/x
To find the bearing of point C from point A, we need to determine the angle between the line AB and the line AC.
To calculate the bearing of a point, we use the concept of bearings which are measured clockwise from the north direction.
Step 1: Draw a diagram
Draw a diagram to help visualize the situation. Place point A as the starting point and point B as the destination after walking 4km on a bearing of 015. Then place point C as the destination after walking an additional 6km on a bearing of 105.
Step 2: Determine the angle between the lines
To find the bearing of point C from point A, we need to find the angle between the line AB and the line AC. This can be done by finding the difference between the bearing angles.
Angle ABC = bearing of B - bearing of A
Angle ABC = 015 - 105
Step 3: Normalize the angle
The angle obtained in the previous step might be negative or greater than 360 degrees. To normalize the angle, we add 360 degrees and take the result modulo 360.
Normalized angle ABC = (015 - 105 + 360) % 360
Step 4: Calculate the bearing of C from A
The bearing of point C from point A is the sum of the bearing of point B from point A and the normalized angle between the lines AB and AC.
Bearing of C from A = bearing of B + normalized angle ABC
Now you can substitute the values:
Bearing of C from A = 015 + normalized angle ABC
Calculate the value of the normalized angle ABC and add it to the bearing of B to find the bearing of C from A.
To find the bearing of point C from point A, we can use the concept of bearings and trigonometry.
Step 1: Draw a diagram to visualize the problem. Place point A, point B, and point C on the diagram, with point A as the starting point.
Step 2: Start at point A and walk 4km on a bearing of 015. This means you are moving in the direction indicated by an angle of 15 degrees clockwise from the north direction (assuming north is 0 degrees).
Step 3: Mark point B at the end of this 4km distance.
Step 4: From point B, walk 6km on a bearing of 105. This means you are moving in the direction indicated by an angle of 105 degrees clockwise from the north direction.
Step 5: Mark point C at the end of this 6km distance.
Step 6: To find the bearing of point C from point A, we need to find the angle between the north direction and the line connecting point A and point C.
Step 7: Draw a line connecting point A and point C.
Step 8: Measure the angle between the line connecting point A and point C and the north direction.
Step 9: The measured angle is the bearing of point C from point A.