the position of point A is 41°N,18°E; point B is 800km due West of A along the same latitude.find the longitude of point B to nearest whole degree. take R= 6400km
To find the longitude of point B, we need to consider the distance traveled and the radius of the Earth.
Let's break down the problem step by step:
Step 1: Calculate the arc length between points A and B
Since point B is 800km due West of A along the same latitude, the arc length can be calculated using the formula:
Arc length = Distance / Radius
Arc length = 800km / 6400km (taking R = 6400km)
Arc length = 0.125 rad
Step 2: Convert the arc length from radians to degrees
To convert from radians to degrees, we use the formula:
Degree = (Arc length * 180) / π
Degree = (0.125 * 180) / π
Degree ≈ 7.17°
Step 3: Determine the longitude of point B
The longitude of point B can be found by subtracting the calculated degree from the longitude of point A.
Longitude of point B = 18°E - 7.17° ≈ 10.83°E
Therefore, the longitude of point B, rounded to the nearest whole degree, is 11°E.