Question

Enugu is 450km due south of Kaduna. Lagos is due west of Enugu and on a bearing of 225 degree from Kaduna. Find the distance between 1.Lagos and Enugu.
2.Lagos and kaduna

Answer 1

We can use the cosine rule to solve this problem. Let A be Kaduna, B be Enugu, and C be Lagos.

1. To find the distance between Lagos and Enugu:

- Firstly, we need to find the angle ABC. Since Lagos is due west of Enugu, the angle ABC is 90 degrees.
- Next, we can use the cosine rule to find the distance AB:
AB^2 = AC^2 + BC^2 - 2AC*BC*cos(ABC)
AB^2 = BC^2 + (450km)^2 - 2BC*(450km)*cos(90)
AB^2 = BC^2 + (450km)^2
AB = sqrt(BC^2 + (450km)^2)

2. To find the distance between Lagos and Kaduna:

- We can use the cosine rule again, this time to find the distance AC:
AC^2 = AB^2 + BC^2 - 2AB*BC*cos(ABC)
AC^2 = (sqrt(BC^2 + (450km)^2))^2 + BC^2 - 2(sqrt(BC^2 + (450km)^2))*BC*cos(90)
AC^2 = 2BC^2 + (450km)^2
AC = sqrt(2BC^2 + (450km)^2)