Respuesta :
We have proved that the triangle formed is scalene triangle.
It is given that latitude and longitude of three cities is given.
We have to prove that the triangle formed by the three cities is a scalene triangle.
What is a triangle ?
A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.
As per the question ;
The Δ formed is a scalene triangle.
Raleigh has latitude and longitude (35.82°N , 78.64°W)
Durham has latitude and longitude (35.99°N , 78.91°W)
Chapel has latitude and longitude (35.92°N , 79.04°W)
Let's represent Raleigh as R , Durham as D and Chapel as C.
Let's check it.
Using the distance formula ;
RD = [tex]\sqrt{(35.99-35.82)^2 + (78.91 - 78.64)^2}[/tex]
RD = [tex]\sqrt{( 0.17^2+ 0.27^2)}[/tex]
RD = [tex]\sqrt{0.102}[/tex]
RD = 0.32
Similarly ;
DC = [tex]\sqrt{0.07^2 + 0.13^2}[/tex]
DC = [tex]\sqrt{0.0218}[/tex]
DC = 0.15
And
RC = [tex]\sqrt{0.10^2 + 0.40^2}[/tex]
RC = 0.41
The sides are all of different lengths, so , we can conclude that this is a scalene triangle.
Thus , the triangle formed by given latitude and longitude of three cities is scalene.
To learn more about triangles click here ;
https://brainly.com/question/2773823
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