Enugu is 450 km due south of Kaduna. Lagos is due west of Enugu and on a bearing 225⁰ from Kaduna.

Question

Find the distance between:
Lagos and Enugu.
Lagos and Kaduna.

Answer 1

To find the distance between Lagos and Enugu, we need to find the distance between Enugu and Kaduna first.

Since Enugu is 450 km due south of Kaduna, we can treat Kaduna as the origin (0,0) on a coordinate plane. Therefore, the coordinates of Enugu would be (0, -450).

Now, since Lagos is 225⁰ from Kaduna, we need to convert the bearing into a direction. A bearing of 225⁰ means that Lagos is southwest of Kaduna. This means that the angle between the line from Kaduna to Lagos and the x-axis is 45⁰ (since southwest is halfway between south and west).

To find the coordinates of Lagos, we can use trigonometry. Since the angle is 45⁰ and the distance between Lagos and Enugu is the same as the distance between Enugu and Kaduna, we can say that Lagos is 450 km away on the x-axis and 450 km away on the y-axis. Therefore, the coordinates of Lagos would be (450, -450).

To find the distance between Enugu and Lagos, we can use the distance formula:
√((x₂ - x₁)² + (y₂ - y₁)²)
√((450 - 0)² + (-450 + 450)²)
√(450² + 0)
√(202,500)
= 450 km

Therefore, the distance between Lagos and Enugu is 450 km.

To find the distance between Lagos and Kaduna, we can use the distance formula as well:
√((x₂ - x₁)² + (y₂ - y₁)²)
√((-450 - 0)² + (450 - 0)²)
√((-450)² + 450²)
√(202,500 + 202,500)
√405,000
= 636.4 km

Therefore, the distance between Lagos and Kaduna is 636.4 km.