In a right triangle, if the length of the adjacent side to angle $\theta$ is $12\mathrm{cm}$ and the length of the hypotenuse is $13\mathrm{cm}$, what is the value of $\cos \left(\theta \right)$?

If $\mathrm{angle}2$ is congruent to $\mathrm{angle}6$ in two right triangles, which of the following statements is true about the ratios of their corresponding sides?

Given a right triangle with sides $a$, $b$, and hypotenuse $c$, and angle $\theta$ opposite side $a$, which of the following correctly expresses $\sin \theta$ in terms of the triangle's sides?

In a right triangle, if one leg measures $4$ ft and the hypotenuse measures $8$ ft, what is the length of the other leg $r$?

Given points $a$ and $b$ on the coordinate plane, which choice of coordinates for points $a^{\text{'}}$ and $b^{\text{'}}$ would help prove that lines $ab$ and $a^{\text{'}}{b}^{\text{'}}$ are perpendicular?

Given a right triangle where one of the acute angles is $x$ and the other acute angle is $y$, if $x=13°$, what is the measure of angle $y$?

In right triangle xyz, if angle $y$ is a right angle and the side opposite angle $x$ has length $5$, the side adjacent to angle $x$ has length $12$, and the hypotenuse has length $13$, what is $sinx$?

In a right triangle, if angle $A$ measures $30°$, what is the measure of angle $B$?

In the context of right triangles, which of the following best describes when the $\tan$ function can be applied to relate a line and an arc?