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

Answer 1

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°.