2. Trigonometric Functions on Right Triangles

In right triangle $ABC$, angle $C$ is the right angle, side $AB$ is $10$ units, and side $BC$ is $6$ units. What is the measure of angle $BAC$? Round to the nearest whole degree.

Given a right triangle with an angle $x$, in which triangle is the value of $x$ equal to ${\tan }^{-1}\left(\frac{3.1}{5.2}\right)$?

Given two right triangles, triangle $PQR$ and triangle $STU$, with right angles at $Q$ and $T$ respectively, which angle has a sine ratio equal to $\frac{p}{q}$?

Given a right triangle with angle $LJK$ at vertex $J$, which equation can be used to find the measure of angle $LJK$ if the length of the side opposite $LJK$ is $a$ and the hypotenuse is $c$?

In a right triangle, if $\sin \theta$ = $\frac{3}{5}$, what is the value of $\cos \theta$?

In right triangle $JKL$, if $cos\left(K\right)$ = $\frac{24}{51}$, what is the length of the side adjacent to angle $K$ if the hypotenuse is $51$?

Given a right triangle QSR with right angle at S, if $qs$ is one leg and $qr$ is the hypotenuse, what is the measure of angle $qsr$ in degrees?

In a circle, the length of an arc intercepted by a central angle is $12mm$. If the radius of the circle is $8mm$, what is the measure of the central angle in radians?

In a circle with center $O$ and radius $20$ inches, if the measure of angle $SOV$ is $72°$, what is the length of minor arc $SV$?

Triangle xyz is isosceles. Angle y measures $a$ degrees. What expression represents the measure of angle x?

Given a circle with center O, points A and B on the circle, and point D on the circle such that arc AB has a measure of $80°$, what is the measure of angle BDA, where BDA is an inscribed angle that intercepts arc AB?

In a right triangle, if one of the non-right angles (angle $6$) measures $141°$, what is the measure of the other non-right angle (angle $5$)?

Given a right triangle with vertices labeled x, z, and w, and angle $xzw$, what is the cosine ratio of angle $xzw$?

Given a right triangle with angle $A$ equal to $50°$ and hypotenuse $c$, which equation can be used to solve for $c$ if the side opposite angle $A$ is $a$ and the side adjacent is $b$?

Given a right triangle, which of the following is equal to $\sin (38°)$?