Answer
l = 10.4
w = 6
Work Step by Step
In Rectangle ABCD
triangle ABD and triangle BDC forms the right triangles.
cos 30 ° = $\frac{length of adjacent}{length of hypotenuse}$
cos 30 ° = $\frac{l}{12}$
By using calculator cos 30° = $\frac{sqrt of 3}{2}$
$\frac{sqrt of 3}{2}$ = $\frac{l}{12}$
l = $\frac{sqrt of 3}{2}$ * 12
=6$\sqrt 3$ = 10.4
l = 10.4
In triangle ADB
sin 30° = $\frac{opposite}{hypotenuse}$
= $\frac{AD}{12}$
= $\frac{w}{12}$
By using calculator sin 30° = $\frac{1}{2}$
therefore $\frac{1}{2}$ = $\frac{w}{12}$
w =$\frac{1}{2}$ * 12 = 6
w = 6
