Let
x-------> the length of the rectangle
y------> the width of the rectangle
d----> the diagonal of the rectangle
we know that
The diagonal forms a pair of 30-60-90 right triangles
Step 1
Find the value of y
\(sin(30)=\frac{y}{d}\)
Solve for y
\(y=sin(30)*d\)
we have
\(sin(30)=\frac{1}{2}\\\\d=30\ in\)
substitute
\(y=\frac{1}{2} *30=15\ in\)
Step 2
Find the value of x
\(cos(30)=\frac{x}{d}\)
Solve for x
\(x=cos(30)*d\)
we have
\(cos(30)=\frac{\sqrt{3}}{2}\\\\d=30\ in\)
substitute
\(x=\frac{\sqrt{3}}{2}*30=15\sqrt{3}\ in\)
therefore
the answer is
\(15\ inches\) by \(15\sqrt{3}\ inches\)
