Using the cosine rule, we can find the distance between Lagos and Enugu:
cos(C) = (a^2 + b^2 - c^2) / (2ab)
where C is the angle between a and b.
Let a be the distance from Kaduna to Lagos, which is cosp(225) * b, where b is the distance from Enugu to Lagos.
Let b be the distance from Enugu to Lagos. We know that Enugu is due south of Kaduna, so the angle between Enugu and Lagos is 90 degrees. Therefore, cos(C) = cos(90) = 0.
0 = (a^2 + b^2 - c^2) / (2ab)
0 = (a^2 + b^2 - (cosp(225)*b)^2) / (2ab)
0 = (a^2 + b^2 - (cos^2(45)*b^2)) / (2ab)
0 = (a^2 + b^2 - (1/2)*b^2) / (2ab)
0 = (2a^2 + b^2) / (2ab)
0 = 2a^2 + b^2
b = sqrt(2a^2)
We also know that Enugu is due south of Kaduna, so the distance between Kaduna and Enugu is simply 450km.
Therefore, we can use the Pythagorean theorem to find a:
a^2 + 450^2 = (cosp(225)*b)^2
a^2 + 450^2 = (cos^2(45)*b^2)
a^2 + 450^2 = (1/2)*b^2
a^2 = (1/2)*b^2 - 450^2
a^2 = (1/2)*(2a^2) - 450^2
a^2 = a^2 - 450^2
450^2 = 0 (not possible)
Therefore, there is no solution to find the distance between Lagos and Kaduna and the distance between Lagos and Enugu.
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 Lagos and Enugu, Lagos and kaduna
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