Question

In a rectangle $ABCD,AB=12cm$ and $\angle BAC={30}^{\circ }$. Calculate the length of side $BC$ and diagonal $AC$.

Answer 1

$\begin{array}{c}\angle BAC={30}^o\\ \tan {30}^o=\frac{BC}{AB}\\ \Rightarrow BC=12\times \frac{1}{\sqrt{3}}=4\sqrt{3}\\ \Rightarrow AC=\sqrt{A{B}^2+B{C}^2}=\sqrt{144+48}=8\sqrt{3}\end{array}$