A town Y is 200KM from town X in a direction of 040 degree.How far is Y east of X
To find out how far Y is east of X, we need to calculate the eastward component of the distance between the two towns.
Given:
Distance between town X and town Y = 200 km
Direction of Y from X = 040 degrees
To calculate the eastward component, we need to find the cosine of the angle between the distance vector and the eastward direction.
In trigonometry, the cosine function gives the ratio of the adjacent side to the hypotenuse for a given angle in a right triangle.
In this scenario, the angle we need to consider is the angle between the distance vector and the eastward direction. To determine this angle, we subtract 040 degrees from 090 degrees (since the eastward direction is at a right angle to the northward direction).
Angle between distance vector and eastward direction = 090 degrees - 040 degrees = 050 degrees.
Now we can calculate the eastward component:
Eastward component = Distance between X and Y * cosine (Angle between distance vector and eastward direction)
Eastward component = 200 km * cos(50 degrees)
Using a calculator to evaluate the cosine of 50 degrees, we find that cos(50 degrees) ≈ 0.6428.
Eastward component ≈ 200 km * 0.6428
Eastward component ≈ 128.56 km
Therefore, town Y is east of town X by approximately 128.56 km.