2. Trigonometric Functions on Right Triangles

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?

Given a right triangle with angle $A$, which of the following expressions can be used to find the measure of angle $A$? Select three options.

In a right triangle, if one of the acute angles measures $62°$, what is the measure of the other acute angle?

A right triangle is shown below. Which ratio gives the cosine of $\angle B$?

Which trigonometric function is typically used to find the angle of elevation from a point on the ground to the top of a building when the height of the building $h$ and the horizontal distance from the building $d$ are known?

Given a right triangle with angle $A$ and sides $a$ (opposite), $b$ (adjacent), and $c$ (hypotenuse), which of the following expressions can be used to find the measure of angle $A$? Select one correct option.

Given that $\cos \left(\theta \right)$ = $\frac{3}{10}$, what is the value of $\sin \left(\theta \right)$ if $\theta$ is an acute angle?

Given two right triangles, $△\mathrm{PQR}$ with sides PQ = $3$, QR = $4$, and RP = $5$, and $△\mathrm{STU}$ with sides ST = $5$, TU = $12$, and US = $13$, which angle has a sine ratio of $\frac{3}{5}$?

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 $cbe$?