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

1 Answer
sankarankalyanam
Mar 25, 2018

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

Explanation:

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#

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