Question

Determine the geographic coordinates of St. John's (NL) and Papeete (Tahiti). Calculate the angular distance (in degrees and radians) and the distance in km between the two cities.

Answer 1

Answer:

Explanation:

Here, geographic coordinates of

St. John's (NL) is latit

The angular distance is 100o

To covert it into radians,

1o = pie/ 180o = 0. 0174444 radians

therefore,

100o =?

multiply 100 with 0. 0174444 we get,

= 1. 7444 radians

Now we have a formula to calculate the distance between these two cities.

Let y is the distance between two cities

Therefore,

Y = (x/360) x 2 x pie x R

Here,

x = angular distance between the cities.

pie = 3. 14

R= radius of earth = 6371km

Hence, by putting these values in the above formula we get,

Y = (100/360) x 2 x 3. 14 x 6371

= (0. 277777) x 40009. 88

= 11113. 82 km

Answer 2

Answer:

θ  = 100°

, θ  = 1. 7444 radians

x= 11113. 82 km

Explanation:

The geographic coordinates of  St. John's (NL) and Papeete (Tahiti) given as

St. John's (NL) is latitude :47°33′41″N and longitude: 52°42′45″W

Papeete (Tahiti) is latitude : 17°32′06″S and longitude : 149°34′11″W

Now convert it into degrees

St. John's longitude is : 52°42′ 45″ W  :

: 52° + 42°/60 + 45°/ 3600

: 52° + 0. 7° + 0. 0125°

: 52. 7125°

Papeete longitude is : 149°34′11″W:

: 149°  + 34°/60 + 11°/3600

: 149°  + 0. 5666°  + 3. 0555°  

: 152. 6221°

Let θ is the angular distance,  

Therefore θ = the difference between the longitude

θ= 152. 6221°  - 52. 7125°  

θ  = 100°

The angular distance is 100°.

Now convert covert it into radians,  

1°  =π / 180°  = 0. 0174444 radians

So

 100°  = 0. 0174444 x 100= 1. 7444 radians

θ  = 1. 7444 radians

Distance between these two cities.

Let x is the distance between two cities given as

x = ( θ/360) x 2 x π x R

θ = angular distance between the cities.

R= Radius of earth = 6371 km

π = 3. 14

Now, by putting these values in the above formula ,

x = (100/360) x 2 x 3. 14 x 6371

x= (0. 277777) x 40009. 88

x= 11113. 82 km