2. Trigonometric Functions on Right Triangles

If you are given two $\mathrm{angles}$ in a $\mathrm{right}\mathrm{triangle}$, what additional information do you need to determine all the $\mathrm{side}\mathrm{lengths}$ of the $\mathrm{triangle}$?

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 angle $cbe$ is one of the non-right angles and the other non-right angle measures $72°$, what is the measure of angle $cbe$?

In right triangle $ABC$, angle $BAC$ measures $56°$. What is the measure of angle $BDC$ if $D$ is a point on $AC$ such that $BD$ is perpendicular to $AC$?

Omar wants to determine $cos\theta$ in a right triangle. If the length of the adjacent side to angle $\theta$ is 5 units and the hypotenuse is 13 units, what is $cos\theta$?

In a right triangle, which pair of angles are $\mathrm{linear}\mathrm{pairs}$?

In a right triangle, if angle $A$ measures $37°$, what is the measure of the other non-right angle $B$?

Given a right triangle DEF with right angle at F, if angle E is one of the acute angles, what is the value of $\sin \left(E\right)$ in terms of the sides of the triangle?

Given two right triangles $△abd$ and $△dca$, which congruency theorem can be used to prove that they are congruent? Choose from: $\text{SSS}$, $\text{ASA}$, $\text{SAS}$, or $\text{AAS}$.

Mary thinks the triangle is equilateral. How would you support or dispute her conjecture using trigonometric functions on right triangles?

In a right triangle, if point A is at $(3,2)$ and point B is at $(3,7)$, what is the vertical change from point A to point B?

$\text{If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are:}$

Given a right triangle where side $LK$ is $7$ units, side $KJ$ is $24$ units, and $LJ$ is the hypotenuse, what is the measure of angle $LKJ$? Round to the nearest whole degree.

In the context of right triangles and their angles, which term best describes a pair of angles that are both $\mathrm{vertical}$ and $\mathrm{supplementary}$?

Given that a transversal cuts two parallel lines and forms angles such that $m\angle 4$ = $55.1°$, what are the measures of $m\angle 5$ and $m\angle 7$?