An aeroplane flies from a town X(29°N, 105°E) to another town Y(86°S, 105°E). Calculate, correct to

JAMB Mathematics 2023 63 views

An aeroplane flies from a town X(29°N, 105°E) to another town Y(86°S, 105°E). Calculate, correct to the nearest km, the distance the aeroplane travelled from town X to town Y. [Take π = 3.142 and R = 6370 km]

  1. 6338 km
  2. 8,864 km
  3. 12,787 km ✓
  4. 10,436 km

Explanation

Step 1: Identify that both have same longitude
X: 29°N, 105°E
Y: 86°S, 105°E
Same longitude means they lie on same meridian

Step 2: Calculate latitude difference
From 29°N to 0° = 29°
From 0° to 86°S = 86°
Total difference = 29° + 86° = 115°

Step 3: Write distance formula along meridian
Distance = (θ/180°) × π × R
where θ = angle difference in degrees

Step 4: Substitute values
Distance = (115/180) × 3.142 × 6370

Step 5: Calculate
= 0.6389 × 3.142 × 6370
= 0.6389 × 20,014.54
= 12,787.29 km
≈ 12,787 km (to nearest km)

pastquestions.ng