We have been given diagram of a triangle. We are asked to write an expression that represents the distance between Seattle and San Francisco.
We will use law of cosines to solve our given problem.
[tex]c^2=a^2+b^2-2ab\text{cos}(C)[/tex], where a, b and c are sides corresponding to angle A, B and C.
Let the distance between Seattle and San Francisco be 'c' and [tex]C=21.4[/tex].
Using law of sines, we can set an equation as:
[tex]c^2=1737^2+1858^2-2(1737)(1858)\text{cos}(21.4)[/tex]
Upon taking square root in both sides, we will get:
[tex]c=\sqrt{1737^2+1858^2-2(1737)(1858)\text{cos}(21.4)}[/tex]
Therefore, we can use the expression [tex]\sqrt{1737^2+1858^2-2(1737)(1858)\text{cos}(21.4)}[/tex] can be used to find distance between Seattle, WA, and San Francisco, CA.
