Kathaana village is 74km northwest of mbusyani village.nguluni village is 42km West of mbusyani.by using scale drawing find the distance between nguluni and kathaana?

To find the distance between Nguluni and Kathaana using a scale drawing, we first need to determine the scale of the drawing. Let's assume that 1 cm on the drawing represents 10 km in real life.

From the information given:
- Mbusyani to Kathaana is 74 km
- Mbusyani to Nguluni is 42 km

On the scale drawing, we can draw a line representing the distance from Mbusyani to Kathaana, which would be 7.4 cm long (74 km divided by 10 km/cm). Similarly, the distance from Mbusyani to Nguluni would be 4.2 cm long.

Now, to find the distance between Nguluni and Kathaana on the scale drawing, we can draw a straight line connecting the endpoints of the lines representing the distances from Mbusyani to each village. This line would be the hypotenuse of a right-angled triangle with sides of 4.2 cm and 7.4 cm.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
Distance = √(4.2^2 + 7.4^2)
Distance = √(17.64 + 54.76)
Distance = √72.4
Distance ≈ 8.5 cm

Therefore, the distance between Nguluni and Kathaana on the scale drawing is approximately 8.5 cm.

1. Draw a scale diagram:

- Choose a suitable scale, such as 1 cm = 10 km.
- Draw a line segment representing the 74 km distance between Mbusyani and Kathaana, and label it as KA.
- Draw a line segment perpendicular to KA at Mbusyani, representing the 42 km distance between Mbusyani and Nguluni, and label it as NG.

2. Measure the distance between NG and KA:

- Using a ruler or measuring tape, measure the distance between the line segment NG and the line segment KA.
- Convert this measured distance back to the actual distance using the scale. For example, if you measured 2 cm, then the actual distance would be 2 cm - 10 km/cm = 20 km.

Therefore, the distance between Nguluni and Kathaana is 20 km.