Both the Galapagos Islands and the island of Naura are on the equator, but the Galapagos Islands are at 90.30°W whereas the island of Naura is at 166.56°E. How far is it from the Galapagos Islands to Naura traveling over the Pacific ocean along the equator, correct to the nearest km?

Question

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Respuesta :

andromache andromache · Answer 1 · 2020-08-16T05:57:33+02:00

Answer:

11521 km

Step-by-step explanation:

The computation is given below:

But prior to reaching the final solution first the following calculations need to be computed

Angle between the Galapagos and Nauru is

= 90.30° + 166.56°

= 256.86°

As we know that the total of angles is 360 degrees

Now the major arc and the minor arc is

= 360° - 256.86°

= 103.14°

So, the angles between galapagos islands is

= 180° - 90.30°

= 89.70°

And, angles between the naura island is

= 180° - 166.56°

= 13.44°

Now the sum of this two island is

= 89.70° + 13.44°

= 103.14°

Therefore The length is

[tex]= \frac{\pi r}{180^{\circ}} \times \theta \\\\ = \frac{6,400 \pi}{180^{\circ}} \times 103.14^{\circ}[/tex]

= 11521 km