Tudu You walk 3 km from the point a on a bearing of 023. He then walk 4km on a bearing of 113 to b what is the bearing of b from a
go back to your post about p,q,r in a plane.
It should help you with this.
show your work if you get stuck.
A boy walk 6km from a point P to a Q on a bearing of 065% he then walk to a point R a distance of 13km on a bearing 146% Calculate to the nearest Kilometers the distance
To find the bearing of point B from point A, we can use the following steps:
Step 1: Draw a diagram to visualize the information.
Step 2: Start at point A and face the direction of the first bearing, which is 023 degrees.
Step 3: Walk 3 km in the direction of the first bearing, which takes you to a new point, let's call it C.
Step 4: From point C, turn to face the second bearing of 113 degrees.
Step 5: Walk 4 km in the direction of the second bearing, which takes you to point B.
Step 6: Now, measure the new angle formed between the line connecting points A and B. This new angle will give us the bearing of B from A.
Step 7: Determine the bearing by subtracting the initial bearing of A (023) from the new angle.
Let's calculate the bearing of B from A:
The initial bearing of A is 023 degrees.
The second bearing of 113 degrees minus the initial bearing of 023 degrees gives us a new angle of 090 degrees.
Therefore, the bearing of B from A is 090 degrees.
To find the bearing of point B from point A, we can use trigonometry and vector addition.
First, let's visualize the problem. Imagine a coordinate system where the starting point A is the origin (0,0). From point A, we walk 3 km on a bearing of 023. This means we are moving 3 km in the direction 23 degrees north of east.
To represent this movement as a vector, we can split it into its x and y components. The x-component represents the distance traveled east or west, and the y-component represents the distance traveled north or south.
To calculate the x-component, we multiply the distance (3 km) by the cosine of the bearing angle. So, x = 3 km * cos(23 degrees).
To calculate the y-component, we multiply the distance (3 km) by the sine of the bearing angle. So, y = 3 km * sin(23 degrees).
Therefore, the coordinates of point B, relative to point A, are (x, y) = (3 km * cos(23 degrees), 3 km * sin(23 degrees)).
Now, from point B, we walk 4 km on a bearing of 113. This means we are moving 4 km in the direction 113 degrees north of east.
We can again calculate the x and y components of this movement. The x-component would be 4 km * cos(113 degrees), and the y-component would be 4 km * sin(113 degrees).
To get the final position, we add the components of the two movements together. So, the x-coordinate of point B is x + 4 km * cos(113 degrees), and the y-coordinate is y + 4 km * sin(113 degrees).
Now we have the coordinates of point B relative to point A. The final step is to calculate the bearing of point B from point A.
To find the bearing, we can use the inverse tangent function. The bearing angle is given by bearing = atan2(y-coordinate, x-coordinate), where atan2 is a function that takes into account the sign of the coordinates to determine the correct quadrant.
Substituting the values, we get the bearing = atan2((y + 4 km * sin(113 degrees)), (x + 4 km * cos(113 degrees))).
Calculating this expression will give us the bearing of point B from point A.