Answer:
[tex]e^2=11^2+9^2-2*11*9*cos(140^o)[/tex]
Step-by-step explanation:
Please find the attachment.
We have been given that in ΔDEF, DE = 11, EF = 9, and angle E = 140°. We are asked to determine the equation that can be used to find the length of third side using law of cosines.
We can use Law of cosines to solve for a side of triangle, when we are given other two sides of the triangle and angle corresponding the side we need to figure out.
[tex]c^2=a^2+b^2-2ac*cos(c)[/tex]
We can see from our attachment that e is side corresponding to angle 140 degrees, so to find the length of we can set an equation as:
[tex]e^2=f^2+d^2-2fd*cos(e)[/tex]
Upon substituting our given values we will get,
[tex]e^2=11^2+9^2-2*11*9*cos(140^o)[/tex]
Therefore, the equation [tex]e^2=11^2+9^2-2*11*9*cos(140^o)[/tex] can be used to find the length of third side.
Let us solve for third side.
[tex]e^2=121+81-198*cos(140^o)[/tex]
[tex]e^2=121+81-198*(-0.766044443119)[/tex]
[tex]e^2=121+81+151.676799737562[/tex]
[tex]e^2=353.676799737562[/tex]
Let us take square root of both sides of our equation.
[tex]e=\sqrt{353.676799737562}[/tex]
[tex]e=18.806\approx 18.81[/tex]
Therefore, the length of 3rd side of triangle DEF is 18.81.
