2. Trigonometric Functions on Right Triangles

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 $m\angle 7$?

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 $\theta$.

Sketch an angle θ in standard position such that θ has the least positive measure, and the given point is on the terminal side of θ. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. See Examples 1, 2, and 4. (―8 , 15)

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 $\sqrt{3}$?

Concept Check What is wrong with the following item that appears on a trigonometry test? "Find sec θ , given that cos θ = 3/2 . "