An aeroplane travelling from town A to town C travels 9km due west to Town B and then 12km due south to town C.

Sketch a diagram to represent the movement of the diagram from Town A to Town C

Calculate the distance between Town A and Town C

Find the total distance covered by the aeroplane in flying from Town A to Town C

Cannot diagram here.

Distance A-C, use Pythagorean theorem.

https://en.wikipedia.org/wiki/Pythagorean_theorem

Total distance = 9 + 12 = ?

To sketch the diagram:

1. Draw a horizontal line from left to right to represent the direction of west-east.
2. Label the left end of the line as Town A and the right end as Town C.
3. Measure a distance of 9cm (or any appropriate scale) to the left of Town C, and draw a vertical line downwards to represent the direction of south.
4. Label the bottom end of the line as Town B.

Now, to calculate the distance between Town A and Town C:
- Use the Pythagorean theorem, as we have a right-angled triangle with sides of 9km and 12km.
- The distance between Town A and Town C can be found using the formula: distance = √(9^2 + 12^2).
- Thus, the distance between Town A and Town C is √(81 + 144) = √225 = 15km.

Finally, to find the total distance covered by the airplane:
- Add the distance of 9km covered in the westward direction to the distance of 12km covered in the southward direction.
- Therefore, the total distance covered by the airplane from Town A to Town C is 9km + 12km = 21km.

To sketch the diagram representing the movement of the airplane from Town A to Town C, draw two lines. The first line, representing the 9km distance due west from Town A to Town B, should be drawn horizontally to the left. The second line, representing the 12km distance due south from Town B to Town C, should be drawn vertically downwards from the end of the previous line. The intersection point of the two lines represents Town C.

To calculate the distance between Town A and Town C, we can use the Pythagorean theorem. The horizontal distance (9km due west) can be considered as the base of a right-angled triangle, and the vertical distance (12km due south) can be considered as the height. Therefore, using the Pythagorean theorem, the distance between Town A and Town C can be calculated as the hypotenuse of this right-angled triangle.

Applying the Pythagorean theorem:
Distance^2 = Base^2 + Height^2
Distance^2 = 9^2 + 12^2
Distance^2 = 81 + 144
Distance^2 = 225
Distance = sqrt(225)
Distance = 15 km

Therefore, the distance between Town A and Town C is 15km.

To find the total distance covered by the airplane in flying from Town A to Town C, we simply add the horizontal distance (9km) and the vertical distance (12km). Thus, the total distance covered is 9km + 12km, which equals 21km.