How do you find the exact value of the third side given $triangle DEF$ , $d=sqrt3$ , e=5, and $mangleF=pi/6$ ?

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Answer 1 · 2018-03-25T09:53:32

$color(indigo)("Exact value of length of side " f = sqrt13$

Given : $d = sqrt3, e = 5, hat F = pi/6, " To find length of side f"$

![https://www.in.pinterest.com/pin/500040364846620813/]( useruploads.socratic.org )

$"Applying Law of cosines"$ ,

$f = sqrt(d^2 + e^2 - (2 * d * e * cos F))$

$f = sqrt((sqrt3)^2 + 5^2 - (2 * sqrt3 * 5 * cos (pi/6)$

$f = sqrt(3 + 25 - (2 * sqrt3 * 5 * (sqrt3/2))) = sqrt(28 - 15) = sqrt13$

How do you find the exact value of the third side given triangle DEFtriangle DEF, d=sqrt3d=sqrt3, e=5, and mangleF=pi/6mangleF=pi/6?