SAT Math: Geometry and Trigonometry

The side length of a square is $55$ centimeters $(\text{cm})$. What is the area, in $\text{cm}^2$, of the square?

The area of a square is $64$ square inches. What is the side length, in inches, of this square?

In $\triangle XYZ$, the measure of $\angle X$ is $24^\circ$ and the measure of $\angle Y$ is $98^\circ$. What is the measure of $\angle Z$?

In triangles $LMN$ and $RST$, angles $L$ and $R$ each have measure $60^{\circ}$, $LN = 10$, and $RT = 30$. Which additional piece of information is sufficient to prove that triangle $LMN$ is similar to triangle $RST$?

In triangles $ABC$ and $DEF$, angles $B$ and $E$ each have measure $27^{\circ}$ and angles $C$ and $F$ each have measure $41^{\circ}$. Which additional piece of information is sufficient to determine whether triangle $ABC$ is congruent to triangle $DEF$?

In the triangle shown, what is the value of $\tan x^{\circ}$?


Note: Figure not drawn to scale.

In triangle $ABC$, angle $B$ is a right angle. The length of side $AB$ is $10\sqrt{37}$ and the length of side $BC$ is $24\sqrt{37}$. What is the length of side $AC$?