The bearing of X from Y is approximately 126.87 degrees.
Calculation of the bearing of X from Y:
Step 1: Diagram and information gathering
We are given the following information:
P is a point.
X is a point due west of P, 10 km away.
Y is a point due south of P, 15 km away.
Step 2: Create a right triangle
Imagine a right triangle with the following sides:
XY (hypotenuse): calculated using the Pythagorean theorem
PX (adjacent to angle at X): 10 km
PY (opposite to angle at X): 15 km
Step 3: Calculate the hypotenuse (XY)
Using the Pythagorean theorem:
XY^2 = PX^2 + PY^2
XY^2 = 10^2 + 15^2
XY = √(100 + 225)
XY = √325
XY ≈ 18.03 km
Step 4: Calculate the angle at X (θ)
We need the angle between PX and XY, which we'll call θ.
We can use the inverse cosine function (cos^-1) to calculate this angle:
cos(θ) = PX / XY
cos(θ) = 10 / 18.03
θ = cos^-1(10 / 18.03)
θ ≈ 53.13°
Step 5: Convert the angle to bearing
Bearings are measured clockwise from the north direction.
Since X is west of Y, the bearing of X from Y is 180 degrees minus the angle calculated in step 4:
Bearing of X from Y = 180° - θ
Bearing of X from Y = 180° - 53.13°
Bearing of X from Y ≈ 126.87°