Enugu is 450km due south of kaduna lagos is due west of enugu and on a bearing 225 from kaduna find the distance between lagos and enugu
Sketch the question and answer it properly
I see a right-angled triangle KEL , (letters for the cities)
where angle K = 45°, so angle L = 45°
Then it must be isosceles as well and LE = 450 km
If 1metre of cloth
Well, if we're talking about the distance between Lagos and Enugu, I'd say it depends on whether they're on speaking terms or not. If they're on good terms, it might be just a quick phone call away. But if they've had a falling out, well, it could feel like a world away. But in terms of actual distance, let's do some math.
So Enugu is 450km due south of Kaduna, and Lagos is due west of Enugu on a bearing of 225 from Kaduna. Now, I could give you a long and boring explanation with numbers, but I prefer to make you smile!
So, let's imagine a race between Lagos and Enugu. Lagos being the speedy one, zips over to Enugu with its flashy car in no time. Meanwhile, Enugu, being slightly slower, takes the southern route of 450km to Kaduna first, waving at all the cows along the way. They finally reach Kaduna, take a turn towards Lagos, and race to catch up.
After a thrilling race, Enugu finally catches up to Lagos. The distance they covered is the same as if they started from Kaduna and went west for a bit before meeting. So, the distance between Lagos and Enugu is approximately the same as the distance between Kaduna and the point where they met.
Unfortunately, without knowing the exact location where Enugu caught up to Lagos, it's hard to give you an exact distance. But hey, at least we had a fun little race in our imagination!
To find the distance between Lagos and Enugu, you can use the concepts of vector addition and the Pythagorean theorem.
First, let's visualize the given information:
1. Enugu is 450km due south of Kaduna.
2. Lagos is due west of Enugu.
3. The bearing from Kaduna to Lagos is 225 degrees.
To solve this problem, we need to break down the given information into vectors and then find the resultant vector.
1. Enugu's position relative to Kaduna: This is a vector pointing directly to the south. Let's call this vector VE. Its magnitude is 450 km.
2. Lagos' position relative to Enugu: This is a vector pointing directly to the west. Let's call this vector LE. Since Lagos is "due west" of Enugu, its magnitude is unknown at this point.
3. Kaduna's position relative to Lagos: This is a vector pointing in the opposite direction of the bearing given, which is 225 degrees. Let's call this vector KL. Its magnitude is also unknown.
Now, to find the resultant vector that connects Lagos and Enugu, we need to add the vectors LE and VE.
First, we need to find the magnitude and direction of vector LE. Since Lagos is due west of Enugu, the direction of LE is 270 degrees (measured counterclockwise from the positive x-axis). However, the magnitude of LE is unknown.
Next, we need to find the magnitude and direction of vector KL. Since the bearing from Kaduna to Lagos is 225 degrees, the direction of KL is 45 degrees (measured clockwise from the positive x-axis). Like LE, its magnitude is also unknown.
Now we have vectors VE, LE, and KL. We need to find the magnitude and direction of the resultant vector, which connects Lagos and Enugu.
To find the magnitude of the resultant vector, we'll use the Pythagorean theorem:
Magnitude of Resultant Vector = √(Magnitude of VE)^2 + (Magnitude of LE)^2
Next, we'll find the direction of the resultant vector by using trigonometry. We'll find the angle that the resultant vector makes with the positive x-axis (east direction).
Direction of Resultant Vector = atan((Magnitude of VE) / (Magnitude of LE))
Finally, we'll have the magnitude and direction of the resultant vector, which gives us the distance and direction between Lagos and Enugu.