2. Trigonometric Functions on Right Triangles

Triangle $BCD$ is rotated $80°$ clockwise about the origin to form $KLM$. If $\angle KLM=30°$, what is the sine of angle $\angle KLM$?

If one angle of a right triangle is $\theta$ such that $\theta =61.8°$, what is the measure of the other non-right angle in degrees?

In a right triangle, if one of the acute angles measures $20°$, what is the measure of the other acute angle?

Given right triangle JKL, where angle $K$ is the right angle, if $\mathrm{JK}$ = $5$, $\mathrm{KL}$ = $12$, and $\mathrm{LJ}$ = $13$, what is the value of $sinJ$?

In a right triangle, if angle 1 is a right angle so $m\angle 1=90°$, what is the measure of angle 2 if the third angle is $45°$?

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 $SV$?