Question

find the missing side of each triangle.Leave your answers in simplest radical form.A √74B3√11C2√21D2√6E√123

Answer 1

In this problem we have two sides of the triangle and one algle that is between the known sides, so we can use the cos law:

$x^2=a^2+b^2-2ab\cos (\theta)$

and in our problem is going to be:

$x^2=5^2+7^2-2(5)(7)\cos (90)$

we know that cos(90) = 0, then the expression will be:

$\begin{gathered} x^2=25+49 \\ x^2=74 \\ x=\sqrt[]{74} \end{gathered}$