Question 1180056: From a place 400m north of course,a student walks from eastward to a place y which is 800m from x.what is the bearing of x and y
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to determine the bearing of point Y from point X:
1. Visualize the Situation:
Imagine point X as the origin.
The student starts 400 meters north of X, let's call this point A.
The student walks eastward to point Y, which is 800 meters from X.
2. Create a Right Triangle:
Draw a line from X to A (400 meters north).
Draw a line from A to Y (800 meters east).
Draw a line from X to Y (the hypotenuse).
This creates a right triangle where:
AX = 400 meters (north)
AY = 800 meters (east)
3. Calculate the Angle:
We want to find the angle between the line XY and the north direction (AX). Let's call this angle θ.
Use the tangent function: tan(θ) = (opposite side) / (adjacent side) = AY / AX
tan(θ) = 800 / 400 = 2
θ = arctan(2) ≈ 63.43 degrees
4. Determine the Bearing:
Since Y is east of X, the bearing will be in the northeast quadrant.
The bearing is measured clockwise from north.
Therefore, the bearing of Y from X is approximately N 63.43° E.
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