Question

Compute the arc length along the surface of the Earth (Radius =6378137 m) between two points separated at an angle of 0.5″ (seconds of arc) subtended at the center of the earth.

Answer 1

Arc length ≈ 1700 m

Explanation:

The arc length can be found using the following relation

A = (θ/360) x (2πr)

Where θ is arc angle in degrees and r is the radius

First convert seconds into degrees

55"/3600 = 0.01527 degrees

A = (0.01527/360) x (2π*6378137)

A ≈ 1700 m

You can also calculate directly through calculator as

A = r*tan(0°0'55")

A ≈ 1700 m

Answer 2

The solution is given in the attachments.