An aeroplane starts from P and flies due west on the same latitude covering a distance of 1232KM to point T. Calculate the difference in angles between P and T
I don't understand the question.
Is the 1232 km distance measured along a "great circle" of the earth, thus the arc length ?
if so, then just use a simple ratio.
Circumference of earth = 40075 km
Ø/360 = 1232/40075
Ø = appr 11.1°
To calculate the difference in angles between points P and T, we need to know the radius of the Earth and the distance along the latitude.
First, let's assume the Earth is a perfect sphere. The radius of the Earth is approximately 6,371 kilometers.
Since the airplane flies due west along the same latitude, it means that the airplane is moving along a circle of latitude. The length of a circle of latitude can be calculated using the formula:
Length = circumference of the Earth * (angle / 360°)
In this case, the length of the circle of latitude covered by the airplane is 1232 kilometers.
To find the angle, we rearrange the formula:
Angle = (Length / Circumference of the Earth) * 360°
Angle = (1232 km / 2 * π * 6371 km) * 360°
Now, let's calculate the difference in angles between P and T.
Since point T is directly west of point P, the difference in angles will be 180° minus the calculated angle.
Difference in angles = 180° - Angle
Now, we can plug in the values and calculate the difference in angles.