Enugu is 450km due south of kaduna. Lagos is due West of enugu and a bearing 225° from kaduna.
Find the distance between:
Lagos and Enugu.
Lagos and Kaduna.
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.