Manyatta Village is 74 km North West of Nyangata Village. Chamwe village is 42 km west of Nyangata. By using an appropriate scale drawing, find the bearing of Chamwe from Manyatta.
call distance Ma to C = n
law of cosines
n^2 = 74^2 + 42^2 - 2*74*42 cos 45
n^2 = 5476 + 1764 - 4395 = 2844
n = 53.3 km
then
sin Ma/42 = sin 45/n
sin Ma = .557
Ma = 33.8
so direction from Ma to C = East + 45 + 33.8 = east + 78.8
or 169 clockwise from North, (about south by east)
To find the bearing of Chamwe from Manyatta, we need to first create a scale drawing that accurately represents the distances and directions between the villages.
Let's assume that we will use a scale of 1 cm = 10 km for our drawing. This means that every 1 cm on the drawing will represent 10 km in real life.
First, draw a line to represent the direction of North. Then, draw a line to represent the direction of West.
Next, starting at the North point, measure and mark a distance of 7.4 cm (since 1 cm represents 10 km) towards the West direction to represent the location of Manyatta village.
From the same North point, measure and mark a distance of 4.2 cm towards the West direction to represent the location of Nyangata village.
Finally, connect the points representing Manyatta and Chamwe with a straight line.
Now, we need to find the bearing of Chamwe from Manyatta. To do this, we can use a protractor or a compass with a built-in protractor.
Place the center of the protractor on the point representing Manyatta and align the zero degree mark with the line connecting Manyatta and Chamwe.
Read the degree measure where the line intersects the protractor. This will give you the bearing of Chamwe from Manyatta.
Note: The bearing is measured clockwise from North. So if the line intersects the protractor at 30 degrees, the bearing would be N30°W.