Question

Using bearing and distance Enugu is 450km due south of kaduna. Lagos is due west of Enugu and on a bearing 225° from kaduna. Find the distances between (a) Lagos and Enugu (b) Lagos and Kaduna​

Answer 1

Answer:

  (a) Lagos and Enugu: 450 km

  (b) Lagos and Kaduna: 450√2 ≈ 636.4 km

Step-by-step explanation:

Given Enugu is 450 km due south of Kaduna, and Lagos is due west of Enugu and on a bearing of 225° from Kaduna, you want the missing distances between the locations.

Triangle

The three locations form a right triangle with the right angle at Enugu. The angle at Kaduna between the bearings of Enugu (270°) and Lagos (225°) is 45°, so this is an isosceles right triangle. One leg of the triangle is 450 km.

The other leg of the triangle, the distance from Enugu to Lagos, is also 450 km. The hypotenuse of the triangle, the distance from Lagos to Kaduna, is 450√2 ≈ 636.4 km.

(a) Lagos to Enugu, 450 km

(b) Lagos to Kaduna, 636.4 km

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Additional comment

A 45°-45°-90° right triangle is one of two "special" right triangles. Its sides have the ratios 1 : 1 : √2. We used that fact here.

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Answer 2

Using bearing, the distances are given as follows;

(a) Lagos and Enugu: 450 km

 (b) Lagos and Kaduna: 450√2 ≈ 636.4 km

How was the above derived?

Since Enugu is 450 km due south of Kaduna, and Lagos is due west of Enugu and on a bearing of 225° from Kaduna, you want the missing distances between the locations.

The three locations form a right triangle with the right angle at Enugu.

The angle at Kaduna between the bearings of Enugu (270°) and Lagos (225°) is 45°, so this is an isosceles right triangle.

One leg of the triangle is 450 km.

The other leg of the triangle, the distance from Enugu to Lagos, is also 450 km. The hypotenuse of the triangle, the distance from Lagos to Kaduna, is 450√2 ≈ 636.4 km.

(a) Lagos to Enugu, 450 km

(b) Lagos to Kaduna, 636.4 km

Learn more about bearing at:

https://brainly.com/question/30916717

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