Question

Suppose that two small cities have the same longitude, which gives the east-west position of a point on Earth's surface. One has latitude 23 degrees north, and the other has latitude 47 degrees. Assume Earth is a sphere with the a radius of 6,380km. Find the distance between the cities to the nearest kilometer.

_______km

Rewrite the arc length formula for an angle measure x given in radians, and simplify.

L=_________

Answer 1

Distance between A and B is 2672 km.

Explanation:

Since one city B is having latitude of 23° and other town is having latitude of 47°.Radius of Earth has been given as 6380 km.

Therefore arc A from x-axis will be A = 2πr(∅/360) = 2×3.14×6380×(47/360)

= 5230.90 km

Now arc B from x-axis = 2πr(∅'/360) = 2×3.14×6380(23/360) = 2559.80 km

Therefore distance between them = 5230.9-2559.8 = 2671.9 ≅ 2672 km

Now we will rewrite the arc length formula in radians.

arc A = r×(∅×π/180)

arc A = 6380×(47×π/180) = 1665.9π

arc B = 6380×(23×π/180) = 815.22π

Now the distance between A and B = 850.68π