Question

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?

Answer 1

11521 km

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

`= (\pi r)/(180^(\circ)) * \theta \\\\ = (6,400 \pi)/(180^(\circ)) * 103.14^(\circ)`

= 11521 km