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
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.