To find the bearing of [tex]\( R \)[/tex] from [tex]\( P \)[/tex], let's break down the steps methodically:
1. Understanding Bearings:
- Bearings are measured clockwise from the north direction.
- A bearing of [tex]\(300^\circ\)[/tex] means that when standing at [tex]\( P \)[/tex] and looking towards [tex]\( Q \)[/tex], the direction [tex]\( Q \)[/tex] is measured as [tex]\(300^\circ\)[/tex] clockwise from the north.
- Similarly, a bearing of [tex]\(210^\circ\)[/tex] from [tex]\( Q \)[/tex] means that when standing at [tex]\( Q \)[/tex] and looking towards [tex]\( R \)[/tex], the direction [tex]\( R \)[/tex] is measured as [tex]\( 210^\circ \)[/tex] clockwise from the north.
2. Summing the Bearings:
- Since the given bearings are stated in terms of their position relative to each other, you can directly add these angles to find the bearing of [tex]\( R \)[/tex] from [tex]\( P \)[/tex].
- Adding these bearings:
[tex]\[
300^\circ + 210^\circ = 510^\circ
\][/tex]
3. Normalize Within 0° to 360°:
- Bearings should always be expressed within the standard range of [tex]\( 0^\circ \)[/tex] to [tex]\( 360^\circ \)[/tex]. To do this, we subtract 360° from any value greater than 360°:
[tex]\[
510^\circ - 360^\circ = 150^\circ
\][/tex]
4. Final Bearing:
- Hence, the bearing of [tex]\( R \)[/tex] from [tex]\( P \)[/tex] is:
[tex]\[
150^\circ
\][/tex]
Therefore, the bearing of [tex]\( R \)[/tex] from [tex]\( P \)[/tex] is [tex]\( 150^\circ \)[/tex].
