2009 年

In the figure, $2AB=3BC$. Find $\theta$ correct to the nearest degree.

In the figure, $ABCD$ is a rectangle. It is given that $E$ is the foot of the perpendicular from $D$ to $AC$. If the area of $\triangle ADE$ is $1\text{ cm}^2$, then the area of $\triangle ABC$ is

In the figure, $ADE$ is a straight line. If $\angle ABC=x$ and $\angle CDE=y$, then $AD=$

If $A$ and $B$ are acute angles such that $A+B=90^\circ$, then $\cos^2 A+\sin^2 B=$

In $\triangle ABC$, $AB:BC:AC=3:4:5$. Find $\tan A:\cos C$.

In the figure, $ABCD$ is a rhombus and $ABE$ is a straight line. If $\angle BCE=40^\circ$ and $BC=CE$, then $\angle CAD=$

If each interior angle of a regular $n$-sided polygon is $144^\circ$, then $n=$

In the figure, $x=$

In the figure, the regular hexagon is divided into six equilateral triangles and two of them are shaded. The number of folds of rotational symmetry of the hexagon is

The coordinates of the point $A$ are $(-3,3)$. If $A$ is reflected with respect to the straight line $x=1$ to the point $B$, then the distance between $A$ and $B$ is