Question

ABCDis a rectangle in which AE line makes 30 degree with angle A which meet DC at E.find AE and EC.

Answer 1

Find AE & EC
Since, dimensions of rectangle are not given by tou, so & will assume it to be l & b.
Consider $\Delta AEM$

$tan{30}^{\circ }=\frac{b}{x}\Rightarrow \frac{1}{\sqrt{3}}=\frac{b}{x}\Rightarrow x=\sqrt{3}b$
$sin{30}^{\circ }=\frac{b}{h}\Rightarrow \frac{\sqrt{3}}{2}=\frac{b}{h}\Rightarrow h=\frac{2b}{\sqrt{3}}$
$\therefore EC=OC-DE$
$=DC-AM$
$\Rightarrow EC=l-x=l-\sqrt{3}b\&AE=\frac{2b}{\sqrt{3}}$