2. Trigonometric Functions on Right Triangles

In a right triangle, if $a$ and $c$ are the lengths of the leg and hypotenuse respectively, which of the following expressions represents $sin\theta$ where $\theta$ is the angle opposite side $a$?

Given a right triangle where $\angle VUW$ = $4x+6$ degrees and $\angle WUT$ = $6x-10$ degrees, what is the value of $x$?

In a right triangle, if two triangles have their corresponding acute angles equal, which angles are congruent to each other?

Rhombus WXYZ is graphed on a coordinate plane with vertices at $(0,0)$, $(4,0)$, $(2,3)$, and $(-2,3)$. What is the perimeter of the rhombus?

In a right triangle, if angle K measures $20°$ and angle L measures $40°$, what is the measure of arc KL on the unit circle corresponding to angle K?

Concept Check Suppose that ―90° < θ < 90° . Find the sign of each function value.

sec(―θ)

A regular $22$-gon is a polygon with $22$ equal sides and angles. What is the measure of each interior angle of a regular $22$-gon? If necessary, round your answer to the nearest tenth. (Use the formula for each interior angle: $\frac{(n-2)\times 180}{n}$ where $n$ is the number of sides.)

Given a right triangle where the length of the side opposite angle $\theta$ is $h=8.1$ inches and the hypotenuse is $k=9$ inches, what is $sin\left(\theta \right)$?

Given two parallel lines cut by a transversal, if the alternate interior angles are $k-10$ degrees and $2k-40$ degrees, what is the value of $k$?

Given that lines a and b are parallel, and lines e and f are also parallel, if angle $m1$ is $89°$, what is the measure of the corresponding angle formed by the intersection of lines e and f with a transversal?

Given a right triangle with points $E$, $F$, $D$, $B$, $C$, and $A$, which angle is a vertical angle with $\angle EFD$?

Given a right triangle where angle $B$ is $152°$, which of the following statements is true?

In Exercises 37–38, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ, or state that the function is undefined.

(0, -1)