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 with diagram

Answer 1

To calculate the bearing from point P to point Q based on the provided coordinates, let's first visualize the points.

1. **Positioning the Points**:
- Point R is the origin (0, 0).
- Point P is positioned 24 meters North of R. So the coordinates of P are (0, 24).
- Point Q is positioned 7 meters East of R. So the coordinates of Q are (7, 0).

2. **Calculating the Bearing**:
- Bearing is typically measured clockwise from north.
- The line from P to Q can be visualized in the Cartesian plane with P at (0, 24) and Q at (7, 0).
- To find the angle, we can use the tangent function and trigonometric ratios.

3. **Finding the Angle**:
- The difference in the East-West (x-axis) direction from P to Q is 7 meters (east).
- The difference in the North-South (y-axis) direction from P to Q is 24 - 0 = 24 meters (south).
- We can determine the angle using the arctangent function:

\[
\theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right) = \tan^{-1}\left(\frac{7}{24}\right)
\]

4. **Calculating the Angle**:
\[
\theta = \tan^{-1}\left(\frac{7}{24}\right) \approx 16.26^\circ
\]

5. **Calculating the Bearing**:
- The bearing from North is measured clockwise. Thus, the bearing will be:
\[
\text{Bearing} = 0^\circ + \theta = 0^\circ + 16.26^\circ \approx 16^\circ
\]
- Rounding to the nearest degree gives us a final bearing of approximately **16°** from North.

### Diagram
A simple description of the diagram:

```
P (0, 24)
|
|
|
|______________ Q (7, 0)
```

In this diagram:
- P is above on the y-axis (North), and Q is on the right on the x-axis (East).
- The angle measured clockwise from the North at point P towards Q forms the angle we've calculated.

### Final Answer
The bearing from point P to point Q is **16°**.