Question
Point p and q are 24m North and 7East of point r respectively what is the bearing of a from p to the nearest degree
Answers
GPT-4o mini
To find the bearing from point \( P \) to point \( Q \) given their positions relative to point \( R \), we first need to establish the positions of the points based on the information provided.
1. **Point \( R \)** is our reference point.
2. **Point \( P \)** is 24 meters North of point \( R \).
3. **Point \( Q \)** is 7 meters East of point \( R \).
Now, we can visualize this on a coordinate system:
- Let point \( R \) be at the origin \((0, 0)\).
- Point \( P \) will be at \((0, 24)\) because it is 24 meters North (positive y-direction).
- Point \( Q \) will be at \((7, 0)\) because it is 7 meters East (positive x-direction).
To find the bearing from point \( P \) to point \( Q \):
1. Calculate the differences in the x and y coordinates:
- Change in x (from \( P \) to \( Q \)): \( 7 - 0 = 7 \)
- Change in y (from \( P \) to \( Q \)): \( 0 - 24 = -24 \)
2. The angle \( \theta \) can be found using the arctangent function:
\[
\theta = \tan^{-1}\left(\frac{\text{change in y}}{\text{change in x}}\right) = \tan^{-1}\left(\frac{-24}{7}\right)
\]
Using a calculator, we compute:
\[
\theta \approx -73.74^\circ
\]
3. The bearing is measured clockwise from North. Since we are in the fourth quadrant (East and South), we must convert this angle to a bearing:
- Bearing = \( 360^\circ + (-73.74^\circ) = 360^\circ - 73.74^\circ = 286.26^\circ \)
Rounding this to the nearest degree:
\[
\text{Bearing from } P \text{ to } Q \approx 286^\circ.
\]
Thus, the bearing from point \( P \) to point \( Q \) is approximately **286°**.
1. **Point \( R \)** is our reference point.
2. **Point \( P \)** is 24 meters North of point \( R \).
3. **Point \( Q \)** is 7 meters East of point \( R \).
Now, we can visualize this on a coordinate system:
- Let point \( R \) be at the origin \((0, 0)\).
- Point \( P \) will be at \((0, 24)\) because it is 24 meters North (positive y-direction).
- Point \( Q \) will be at \((7, 0)\) because it is 7 meters East (positive x-direction).
To find the bearing from point \( P \) to point \( Q \):
1. Calculate the differences in the x and y coordinates:
- Change in x (from \( P \) to \( Q \)): \( 7 - 0 = 7 \)
- Change in y (from \( P \) to \( Q \)): \( 0 - 24 = -24 \)
2. The angle \( \theta \) can be found using the arctangent function:
\[
\theta = \tan^{-1}\left(\frac{\text{change in y}}{\text{change in x}}\right) = \tan^{-1}\left(\frac{-24}{7}\right)
\]
Using a calculator, we compute:
\[
\theta \approx -73.74^\circ
\]
3. The bearing is measured clockwise from North. Since we are in the fourth quadrant (East and South), we must convert this angle to a bearing:
- Bearing = \( 360^\circ + (-73.74^\circ) = 360^\circ - 73.74^\circ = 286.26^\circ \)
Rounding this to the nearest degree:
\[
\text{Bearing from } P \text{ to } Q \approx 286^\circ.
\]
Thus, the bearing from point \( P \) to point \( Q \) is approximately **286°**.