Question

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

Answer 1

`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"`

`"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`