Question
The bearing Q from P is 300° and the bearing of R from Q is 210°.
If Q is equidistance from P and R, find the bearing of R
If Q is equidistance from P and R, find the bearing of R
Answers
GPT-4o mini
To find the bearing of point R from point P, we start with the given information:
1. The bearing of Q from P is 300°.
2. The bearing of R from Q is 210°.
3. Q is equidistant from P and R.
Let's break this down into a clear solution:
1. **Understanding Bearings:**
- Bearings are given in degrees from the north direction (0°), measured clockwise.
- A bearing of 300° indicates that when you stand at point P, you face north (0°) and turn clockwise to 300° to face point Q.
- A bearing of 210° means when you are at point Q, you face north and turn clockwise to 210° to face point R.
2. **Drawing the Situation:**
- From point P, draw a line to Q making a 300° angle from north.
- From point Q, draw a line to point R at a 210° angle from north.
3. **Finding the Angle at Q:**
- The angle between the line PQ and the line QR can be calculated as follows:
- From north (0°), the bearing from P to Q is 300°.
- From north (0°), the bearing from Q to R is 210°.
- The angle between these lines is calculated by subtracting the bearing of Q from P from the bearing of R from Q.
4. **Calculating Bearings:**
\[
\text{Angle} = 300° - 210° = 90°
\]
5. **Finding the Bearing of R from P:**
- Since the angle at Q is 90°, we can continue clockwise from PQ (keeping in mind that we need to calculate the bearing from P to R).
- From P to Q is 300°, and moving 90° clockwise will give us the bearing from P to R:
\[
\text{Bearing of } R \text{ from } P = 300° + 90° = 390°
\]
Since bearings are typically expressed in the range of 0° to 360°, we subtract 360°:
\[
390° - 360° = 30°
\]
Therefore, the bearing of R from P is **30°**.
1. The bearing of Q from P is 300°.
2. The bearing of R from Q is 210°.
3. Q is equidistant from P and R.
Let's break this down into a clear solution:
1. **Understanding Bearings:**
- Bearings are given in degrees from the north direction (0°), measured clockwise.
- A bearing of 300° indicates that when you stand at point P, you face north (0°) and turn clockwise to 300° to face point Q.
- A bearing of 210° means when you are at point Q, you face north and turn clockwise to 210° to face point R.
2. **Drawing the Situation:**
- From point P, draw a line to Q making a 300° angle from north.
- From point Q, draw a line to point R at a 210° angle from north.
3. **Finding the Angle at Q:**
- The angle between the line PQ and the line QR can be calculated as follows:
- From north (0°), the bearing from P to Q is 300°.
- From north (0°), the bearing from Q to R is 210°.
- The angle between these lines is calculated by subtracting the bearing of Q from P from the bearing of R from Q.
4. **Calculating Bearings:**
\[
\text{Angle} = 300° - 210° = 90°
\]
5. **Finding the Bearing of R from P:**
- Since the angle at Q is 90°, we can continue clockwise from PQ (keeping in mind that we need to calculate the bearing from P to R).
- From P to Q is 300°, and moving 90° clockwise will give us the bearing from P to R:
\[
\text{Bearing of } R \text{ from } P = 300° + 90° = 390°
\]
Since bearings are typically expressed in the range of 0° to 360°, we subtract 360°:
\[
390° - 360° = 30°
\]
Therefore, the bearing of R from P is **30°**.