Mohammedwalks 3km from pointA on a bearingof023 he thenwalks 4km on a bearing of 113 to a point B what is the bearing of B from A
you walk on a heading, not a bearing.
If A is at (0,0) then his first turn is at
X is at A+(3sin23° , 3cos23°) = (1.172,2.761)
and B is at X + (4cos23° , -4sin23°) = (4.854,1.198)
so the bearing of B from A is θ, where tanθ = 4.854/1.198 ≈ 76°
Well, if Mohammed is walking around with bearings, maybe he should consider becoming a human compass! Anyway, let's figure this out.
Mohammed starts at point A and walks 3km on a bearing of 023. That means he's moving mostly north-northeast.
Then, he walks 4km on a bearing of 113. This takes him somewhere south-southeast, but still in a generally northeastern direction.
So, to find the bearing of point B from point A, we can imagine connecting these two points with a straight line. This line would be pointing somewhere between north and northeast, but leaning more towards northeast.
Therefore, the bearing of point B from point A would be something like 045, which is between north and northeast. Just remember that Mohammed might be great at compass readings, but we're talking about him, not the actual compass!
To find the bearing of point B from point A, we can use trigonometry. First, let's draw a diagram to visualize the situation:
```
A
|\ 3km
| \ 023°
| \
| \
| \
| \
| \ 4km
| \
B | \
```
We know that Mohammed walks 3km on a bearing of 023° from point A. This means he walks in a direction that is 23° east of due north.
Next, Mohammed walks an additional 4km on a bearing of 113° to reach point B. This means he walks in a direction that is 113° east of due north.
To find the bearing of point B from point A, we need to add the two angles together.
023° (bearing of point A) + 113° (change in bearing from point A to point B) = 136°.
So, the bearing of point B from point A is 136°.
To find the bearing of point B from point A, we need to calculate the angle between the line connecting the two points and the north direction.
First, let's draw a diagram to visualize the situation.
```
N
|
|
|
W----A----B
|
|
|
S
```
Here, A represents point A and B represents point B. N, S, E, and W are the cardinal directions.
Now, we can break down the problem into two components:
1. Mohammed walks 3km on a bearing of 023 from point A.
2. Mohammed then walks 4km on a bearing of 113 to reach point B.
To find the bearing of B from A, we need to add the initial bearing of 023 to the change in bearing from A to B.
Initial bearing from A = 023 degrees
Change in bearing from A to B = 113 - 023 degrees
Adding these values gives us the bearing of B from A:
Bearing of B from A = 023 + (113 - 023) degrees
Bearing of B from A = 023 + 090 degrees
Bearing of B from A = 113 degrees
Therefore, the bearing of point B from point A is 113 degrees.