College

If \(\theta = 27^\circ\), find the distance between two cities, A and B, to the nearest mile. The radius of the Earth is approximately 4000 miles.

Answer :

The distance between two cities, A and B is 1884 miles. The solution has been obtained using the concept of arc of circle.

What is arc of circle?

A circle's arc is referred to as a section or portion of its circumference. A chord of a circle is a straight line that can be created by joining the arc's two ends. A semicircular arc is one whose length is exactly half that of the circle.

We are given that the angle is 27° and radius is 4000 miles

We know that circumference of circle = 2πr

So,

C=2*3.14*4000

C= 25120

Now, to find the length of arc AB,

⇒Arc length = (27° × 25120)/360°

Arc length = 1884

Hence, the distance between two cities, A and B is 1884 miles.

Learn more about arc of circle from the given link

https://brainly.com/question/28108430

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