Question

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? A 2,300 miles B. 1,518 miles C. 1,233 miles D. 1,052 miles E. 998 miles

Answer 1

THE ANSWER 

let be S1 = Serravalle
S2= San Marino and 
S3= Chiesanuova

for finding the distance Chiesanuova from Serravalle,

(distance S1 to  S2)  +  (distance S2 to S3) = 982 miles + 833 miles =1.815 miles

the answer is B. 1, 815 miles

Answer 2

The distance between Chiesanuova and Serravalle is 1,518 miles. Therefore, option B is the correct answer.

Given that, the distance from Serravalle to San Marino is 982 miles, and the distance from Chiesanuova to San Marino is 833 miles.

What is the cosine formula?

The cosine formula to find the side of the triangle is given by c²=a²+ b²– 2ab cos C. Where a,b and c are the sides of the triangle.

Here, we have two sides of the triangle and one of its angles.

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

Then we use the cosine theorem to find x.

x²=b²+c²-2bc cos θ

Now, put b=833 and c=982 and θ=113.23° in the cosine formula and simplify.

So, x²=833²+982²-2×833×982 cos 113.23°

⇒x=1,517.73 miles

⇒x=1,517.73≈1,518

The distance between Chiesanuova and Serravalle is 1,518 miles. Therefore, option B is the correct answer.

To learn more about the cosine rule visit:

https://brainly.com/question/20839703.

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