2. Trigonometric Functions on Right Triangles

Given a right triangle with vertices at $(0,0)$, $(4,0)$, and $(4,3)$, let point $z$ be $(4,0)$ and line $ab$ be the segment from $(0,0)$ to $(4,0)$. Which of the following points lies on the line that passes through point $z$ and is perpendicular to line $ab$?

In a right triangle, what is the tangent ratio for angle $\theta$?

Given points $a$ and $b$ on the coordinate plane, which choice of coordinates for points $a^{\text{'}}$ and $b^{\text{'}}$ would help prove that lines $ab$ and $a^{\text{'}}{b}^{\text{'}}$ are perpendicular?

Given a right triangle with angle $gfe$, where the side adjacent to angle $gfe$ has length $a$ and the hypotenuse has length $h$, which equation can be used to find the measure of angle $gfe$?

In circle t, if $\angle \mathrm{PTQ}$ is inscribed and $\angle \mathrm{RTS}$ is a central angle that intercepts the same arc, what is the measure of $\angle \mathrm{PTQ}$ if $\angle \mathrm{RTS}$ measures $66°$?

If point $z$ is equidistant from the sides of triangle $RST$, which of the following must be true?

A regular polygon has $8$ sides. What is the measure of each interior angle?

In a right triangle EFD, angle $F$ is the right angle, and the lengths of sides $EF$ and $FD$ are $3$ and $4$ units respectively. What is the measure of angle $EFD$ (in degrees)?

Given that $m\angle \mathrm{CED}=72°$ and $m\angle \mathrm{AEB}=7x-2°$, what is the value of $x$ if $m\angle \mathrm{CED}$ and $m\angle \mathrm{AEB}$ are complementary angles?

Which of the following correctly expresses the sine of angle $\theta$ in a right triangle in terms of the lengths of the sides?

Which equation correctly relates the measure of angle ${\theta }_1$ in a right triangle to the lengths of the opposite side $O$ and the hypotenuse $H$?

Given a right triangle where the measure of angle $\angle 6$ is $32°$, what is the sum $m\angle 4+m\angle 5$ in degrees?

In right triangle $△abc$, if side $ac$ = $5$ mm, side $ab$ = $3$ mm, and side $bc$ = $4$ mm, what is $\sin a$?

In a right triangle, what is the definition of $\sin$ of an angle $\theta$?

Which of the following expressions can be used to find the measure of angle $B$ in a right triangle if the lengths of the sides opposite and adjacent to $B$ are known?