Apply the formula for the circumference of a parallel of latitude.

You're on a roll — here's the solution to your problem. We'll use the Earth's radius R = 6371 km. i) Calculate the circumference of the line of latitude 50^ N. Step 1: Apply the formula for the circumference of a parallel of latitude. The formula is C_lat = 2 R , where is the latitude. Here, = 50^ N. C_50^ N = 2 (6371 km) (50^) Step 2: Calculate the numerical value. C_50^ N = 2 (6371) × 0.6427876 C_50^ N ≈ 25732.5 km The circumference of the line of latitude 50^ N is 25733 km (rounded to the nearest kilometer). ii) Calculate the shortest distance PQ, measured along the line of latitude. Points P and Q are on the same latitude 50^ N. Longitude of P is 10^ W. Longitude of Q is 50^ E. Step 1: Determine the difference in longitude. The difference in longitude is 10^ + 50^ = 60^. Step 2: Apply the formula for distance along a parallel of latitude. The formula is D = ()/(360^) × C_lat, where C_lat is the circumference calculated in part (i). D_PQ = (60^)/(360^) × 25732.5 km D_PQ = (1)/(6) × 25732.5 km D_PQ ≈ 4288.75 km The shortest distance PQ along the line of latitude is 4289 km (rounded to the nearest kilometer). iii) Calculate the latitude at which the circumference of the circle of latitude is equal to (1)/(4) the length of the equator. Step 1: Set up the equation based on the given condition. Let the unknown latitude be . The circumference of a parallel of latitude is C_lat = 2 R . The length of the equator is C_eq = 2 R. We are given C_lat = (1)/(4) C_eq. 2 R = (1)/(4) (2 R) Step 2: Solve for . Divide both sides by 2 R: = (1)/(4) = 0.25 Step 3: Find the latitude . = (0.25) ≈ 75.522^ The latitude at which the circumference of the circle of latitude is equal to (1)/(4) the length of the equator is 75.5^ (rounded to one decimal place). What's next?