From a point z 60m north of x a man walks eastwards to another point y 120m from find the bearing of y and x
Guestion
To find the bearing of point Y from point X, we can use trigonometry.
Since point Z is 60m north of point X, the distance between X and Y remains the same, and the man walks eastwards, we can represent the situation as shown:
Z(60m)
|
|
X ------ Y(120m)
Now, let's draw a right-angled triangle triangle XYZ, where:
- Side XZ represents the north-south direction (vertical side)
- Side YZ represents the east-west direction (horizontal side)
Given that XZ = 60m and XY = 120m, we can use the tangent function to find the angle ZXY, which will give us the bearing of point Y from point X.
tan(ZXY) = (opposite side) / (adjacent side)
tan(ZXY) = XZ / XY
tan(ZXY) = 60 / 120
tan(ZXY) = 0.5
To find the angle ZXY, we can find the inverse tangent (or arctan) of 0.5:
ZXY = arctan(0.5)
ZXY ≈ 26.57 degrees
Therefore, the bearing of point Y from point X is approximately 26.57 degrees.
To find the bearing of point Y from point X, we need to determine the angle between the line connecting X and Y and the north direction.
First, let's plot the information provided on a coordinate system.
Let's assign coordinates to the points:
- X: (0, 0)
- Z: (0, 60)
- Y: (120, ?)
Given that point Z is 60 meters north of point X, we can determine that the y-coordinate of Z is 60.
Next, we know that point Y is 120 meters from point X. From the point Z, the man walks eastwards towards point Y, which means the x-coordinate of Y is 120.
Using the coordinates of Y, we can calculate the y-coordinate. Since point Y is 120m away from point X, we can use the Pythagorean theorem to find the distance between Y and Z:
120^2 = 60^2 + y^2
14400 = 3600 + y^2
y^2 = 14400 - 3600
y^2 = 10800
y = sqrt(10800)
y ≈ 103.92
Now that we have the coordinates of point Y as (120, 103.92), we need to find the angle between the line connecting points X and Y and the north direction.
To find the bearing, we need to calculate the arctan of the ratio between the y-coordinate difference (103.92) and the x-coordinate difference (120).
Bearing = arctan(103.92/120)
Using a calculator or a tool that can calculate arctan, the approximate angle is 40.60 degrees.
Therefore, the bearing of point Y from point X is approximately 40.60 degrees.
if you mean the bearing of y from x, then
(a) draw a diagram
(b) the bearing θ is such that tanθ = 120/60