Question

The difference in the length of an arc and its subtended chord on earth’s surface for a distance of 18.5 km is about

Answer 1

0.649 cm

Step-by-step explanation:

Radius of earth = 6371 km

Length of Arc = 18.5 km

Therefore

perimeter of earth /36o =length of arc/subtended angle assume X

Or 2 * pi *r /360= 18.5 / Angle X

Here r = 6371 km , pi = 22/7

Angle X = 0.1663075584

Now as per attached diagram the value of straight chord = 2*6371*1.451306723/1000

Or chord length = 18.49255026 km

Arc length ( given ) = 18. 5 km

Difference = 7.449 m

However , this value may vary as per the value of pi , if taken exact , the difference may be only 0.649 cm.

Answer 2

Answer:

7.449 m

Step-by-step explanation:

Radius of earth = 6371 km

Length of Arc = 18.5 km

Therefore

perimeter of earth /36o =length of arc/subtended angle assume X

Or 2 * pi *r /360. = 18.5 / Angle X

Here r = 6371 km , pi = 22/7

Angle X = 0.1663075584

Now as per attached diagram the value of straight chord = 2*6371*1.451306723/1000  

Or chord length = 18.49255026 km  

Arc length ( given ) = 18. 5 km

Difference = 7.449 m

However , this value may vary as per the value of pi , if taken exact , the difference may be only 0.649 cm.