Answered

From everyday questions to specialized queries, IDNLearn.com has the answers. Get the information you need from our community of experts, who provide detailed and trustworthy answers.

City A is due north of City B. Find the distance between City A ​( north​ latitude) and City B ​( north​ latitude). Assume that the radius of Earth is 3960 miles.


The distance between City A and City B is ___miles.


Can someone help?! Show me step by step how this is done that I can understand it better.

City A Is Due North Of City B Find The Distance Between City A North Latitude And City B North Latitude Assume That The Radius Of Earth Is 3960 MilesThe Distanc class=

Sagot :

Answer:  1679

=========================================================

Explanation:

The notation [tex]47^{\circ}4'[/tex] means "47 degrees, 4 minutes". The "minutes" isn't referring to a time value, but instead they are arc minutes. If we divide one degree into 60 equal pieces, then we form 60 arc minute slices. So in a sense, we are using a round analogue clock to help connect the two ideas.

We can convert to purely degrees through using this formula here

[tex]a^{\circ}b' = a + \frac{b}{60}[/tex]

So,

[tex]47^{\circ}4' = 47 + \frac{4}{60} \approx 47.06667^{\circ}[/tex]

and similarly,

[tex]22^{\circ}46' = 22+ \frac{46}{60} \approx 22.76667^{\circ}[/tex]

Now subtract the two results we got

47.06667-22.76667 = 24.3

The angular distance between the two cities is 24.3 degrees. By "angular distance" I basically mean how far you need to rotate your viewing angle when looking from city A to city B. Imagine that you're able to be situated at the center of the earth.

The circumference of the earth is

C = 2*pi*r

C = 2*pi*3960

C = 24,881.4138164311

which is approximate and the units are in miles. We multiply by the fraction 24.3/360 to find the arc distance along the curve that corresponds to the angle 24.3 degrees. This is because we don't want the whole circumference, but just a small fraction of it.

So (24.3/360)*24,881.4138164311 = 1,679.4954326091

This rounds to 1679

The distance between the two cities is about 1679 miles.

Sqdancefanidn

9514 1404 393

Answer:

  1679 miles

Step-by-step explanation:

One minute is 1/60 of a degree, so the difference in latitudes is ...

  47 4/60 -22 46/60 = 24 18/60 = 24.3 . . . degrees

The arc length is given by ...

  s = rθ . . . . . . r = radius, θ = angle in radians

180° is π radians, so the surface distance between the two cities is ...

  s = (3960 mi)(24.3×π/180) = 534.6π mi ≈ 1679.495 mi

The distance between City A and City B is about 1679 miles.

_____

Additional comment

As a good approximation, the distance is about 60 nautical miles per degree of latitude. Using that approximation, and converting from nautical miles to statute miles would give a distance of 1678 miles.

We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. IDNLearn.com is your reliable source for accurate answers. Thank you for visiting, and we hope to assist you again.