A ship sets sail from port A (86°N, 56°W) for port B (86°N, 64°W), which is close by. Find the dista
A ship sets sail from port A (86°N, 56°W) for port B (86°N, 64°W), which is close by. Find the distance the ship covered from port A to port B, correct to the nearest km. [Take π = 3.142 and R = 6370 km] [sin 56° = 0.8290, cos 56° = 0.5592, tan 56° = 1.4826] [sin 64° = 0.8988, cos 64° = 0.4384, tan 64° = 2.0503] [sin 86° = 0.9976, cos 86° = 0.0698, tan 86° = 14.3007]
Step 1: Identify same latitude
A: 86°N, 56°W
B: 86°N, 64°W
Same latitude means distance along parallel of latitude
Step 2: Calculate longitude difference
Difference = 64° – 56° = 8°
Step 3: Write formula for distance along parallel
Distance = (Δλ/180°) × π × R × cos(φ)
where Δλ = longitude difference, φ = latitude
Step 4: Substitute values
Distance = (8/180) × 3.142 × 6370 × cos(86°)
= (8/180) × 3.142 × 6370 × 0.0698
Step 5: Calculate
= 0.0444 × 3.142 × 6370 × 0.0698
= 0.0444 × 20,014.54 × 0.0698
= 62.02 km
≈ 62 km (to nearest km)
Was this explanation helpful?