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A navigator marks three locations on a satellite map as shown. If the distance from Serravalle to San Marino is 982 miles, and the distance from Chiesanuova to San Marino is 833 miles, then how far is Chiesanuova from Serravalle?

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luisejr77 luisejr77 · Answer 1 · 2019-06-08T03:14:09+02:00

Answer:

The distance from Chiesanuova to Serravalle is 1517.73 miles

Step-by-step explanation:

We have two sides of the triangle and one of its angles.

Call c and b the lengths of the known sides and call x the distance we want to find.

Then we use the cosine theorem to find x

[tex]x^2=c^2 +b^2 -2cbcos(\theta)[/tex]

In this case

[tex]c=982\\b=833\\\theta = 113.23\°[/tex]

So

[tex]x = \sqrt{982^2 + 833^2 -2*(982)(833)cos(113.23\°)}\\\\x =1517.73\ miles[/tex]

eudora eudora · Answer 2 · 2019-06-25T20:27:52+02:00

Answer:

Distance between Chiesanuova and Serravalle is 1517.73 miles.

Step-by-step explanation:

In the given triangle Seravalle, Chiesanuova and San Marino are based at three different vertices S, C and M.

Distance SM = 982 miles

Distance CM = 833 miles

Then we have to calculate the distance CS.

We will apply cosine rule to calculate the distance CS.

CS² = CM²+ MS² - 2(CM)(MS)cos(113.23)

CS² = 982² + 833² - 2(833)(982)(-0.39442)

= 964324 + 693889 + 645280.948

= 2303493.95

CS = √2303493.95 = 1517.73 miles

Therefore, distance between Chiesanuova and Serravalle is 1517.73 miles.