Answer
$x=4$
$A=60^o
\\B=90^o
\\C=30^o$
Work Step by Step
RECALL:
Two similar triangles have:
(1) corresponding angles that are congruent; and
(2) sides that are proportional
Since corresponding angles are congruent, then
$A=60^o
\\B=90^o
\\C=30^o$
Corresponding sides of similar triangles are proportional.
Thus,
$\dfrac{8}{4}=\dfrac{x}{2}$
Cross-multiply to obtain:
$\begin{array}{ccc}
&4(x) &= &8(2)
\\&4x &= &16
\\&\frac{4x}{4} &= &\frac{16}{4}
\\&x &= &4\end{array}$
