2. Trigonometric Functions on Right Triangles

Given a right triangle where one of the acute angles is $x$ and the lengths of the sides opposite and adjacent to $x$ are $3$ and $4$ respectively, what is the value of $x$ in degrees?

In a right triangle, if the length of the adjacent side to angle $x$ is $5$ units and the hypotenuse is $13$ units, what is the value of $\cos \left(x\right)$?

Given a right triangle with hypotenuse of length $c$ and an acute angle $\theta$, express the lengths of the side adjacent to $\theta$ (labeled $a$) and the side opposite $\theta$ (labeled $b$) in terms of $c$ and $\theta$.

In a right triangle, if the length of the adjacent side is $1$ and the length of the opposite side is $\sqrt{3}$, what is the measure of the angle (in degrees) opposite the side of length $\sqrt{3}$?

In circle O, if arc AB measures $48°$, what is the measure of angle CAB, where C is a point on the circle such that angle CAB is an inscribed angle that intercepts arc AB?

Given a right triangle with angle $\mathrm{FGE}$ and the side opposite to $\mathrm{FGE}$ has length $a$, the side adjacent to $\mathrm{FGE}$ has length $b$, and the hypotenuse has length $c$, which equation can be used to find the measure of angle $\mathrm{FGE}$?

In right triangle $PQR$, if angle $Q$ is the right angle, side $PQ$ = $7$ and side $QR$ = $8$, what is the measure of angle $R$? Round to the nearest degree.

In right triangle $△PQR$, the angle bisector of $\angle PQR$ is $QE$. If $m\angle PQE=20°$, what is the measure of $\angle PQR$?

Given a right triangle EGF with $\angle G$ as the right angle, if the side opposite $\angle E$ is $7$ units and the side adjacent to $\angle E$ is $9$ units, which is the best approximation for the measure of $\angle EGF$?

If an angle in a right triangle measures $x$ degrees, what is the measure of its supplement?

Given a right triangle $ABC$ and its translated image $A\text{'}B\text{'}C\text{'}$, which of the following statements is true?

Which of the following statements about $\mathrm{secants}$ and $\mathrm{chords}$ in a $\mathrm{right}\mathrm{triangle}$ is true?

In right triangle QRS, if angle $Q$ is the right angle and side $QR$ has length $6$ and side $QS$ has length $10$, what is the value of $\sin \left(S\right)$?

In kite KLMN, if angle K is $49°$ and angle L is $99°$, what is the measure of angle LMN?

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