Enugu is 450km due south of kaduna. Lagos is due West of enugu and a bearing 225° from kaduna.

Question

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

Answer 1

To find the distance between Lagos and Enugu, we can use the cosine rule for triangles:

Distance^2 = Lagos-Enugu^2 + Lagos-Kaduna^2 - 2(Lagos-Enugu)(Lagos-Kaduna)cos(225°)

Distance^2 = 450^2 + x^2 - 2(450)(x)cos(225°)

Distance^2 = 450^2 + x^2 - 900x(cos(225°))

Since cos(225°) = -√2/2,

Distance^2 = 450^2 + x^2 + 450√2(x)

Next, to find the distance between Lagos and Kaduna:

Distance^2 = Lagos-Kaduna^2 + Kaduna-Enugu^2 - 2(Lagos-Kaduna)(Kaduna-Enugu)cos(180°)

Distance^2 = x^2 + 450^2 - 2(x)(450)cos(180°)

Distance^2 = x^2 + 450^2 - 2(450)(x)

Distance^2 = x^2 + 450^2 - 900x

Now, you can solve for x to find the distances between Lagos and Enugu and between Lagos and Kaduna.