Calculate the shortest distance between two points on Earth using their latitude and longitude coordinates.

Here are the solutions to the given navigation problems: a) Calculate the distance in KM from A to B along a parallel of latitude. Step 1: Identify the given coordinates and constants. Latitude () = 60^ N Longitude of A = 20^ E Longitude of B = 160^ W Radius of Earth (R) = 6370 km = (22)/(7) Step 2: Calculate the difference in longitude (). Since the longitudes are on opposite sides (East and West), we add them: = 20^ + 160^ = 180^ Step 3: Use the formula for distance along a parallel of latitude. The formula is: Distance = ()/(360^) × 2 R Step 4: Substitute the values into the formula and calculate. Distance = (180)/(360) × 2 × (22)/(7) × 6370 × 60^ Distance = (1)/(2) × 2 × (22)/(7) × 6370 × 0.5 Distance = (22)/(7) × 6370 × 0.5 Distance = 22 × 910 × 0.5 Distance = 10010 km The distance from A to B along a parallel of latitude is 10010 km. b) Shortest distance from A to B along a great circle in nautical miles. Step 1: Identify the coordinates. Point A: (60^ N, 20^ E) Point B: (60^ N, 160^ W) Step 2: Calculate the angular distance (D) along the great circle. The formula for the angular distance between two points (L_1, _1) and (L_2, _2) is: D = L_1 L_2 + L_1 L_2 (_2 - _1) Here, L_1 = L_2 = 60^ and the difference in longitude (_2 - _1) = 180^. D = 60^ 60^ + 60^ 60^ 180^ D = (sqrt(3)2)^2 + ((1)/(2))^2 (-1) D = (3)/(4) - (1)/(4) D = (2)/(4) = (1)/(2) Therefore, D = ^-1((1)/(2)) = 60^. Step 3: Convert the angular distance to nautical miles. One degree of a great circle