2. Trigonometric Functions on Right Triangles

Determine whether each statement is possible or impossible. See Example 4. cot θ = ―6

Given a right triangle, what is the measure of angle $A$ if $m\angle A$ is the smallest angle and the other two angles are $90°$ and $71°$?

In triangle MNO, angle MNO measures $112°$. If triangle MNO is a right triangle with the right angle at vertex N, what is the measure of angle LMN?

In a right triangle, what is the reciprocal of $\tan b$?

Given a right triangle with an angle of $35°$ and an adjacent side of length $5$, which equation can be used to solve for the hypotenuse $c$?

In a right triangle, one leg measures $7$ units and the other leg measures $12$ units. Find the measure of the angle opposite the side of length $7$ to the nearest degree.

Given a circle with circumference $C$ and a central angle of $\theta$ radians, what is the length of the arc subtended by the angle $\theta$?

In a triangle, if one angle measures $130°$, which of the following statements is true about the triangle and its angles?

Given a right triangle where one of the acute angles is $52°$ and the hypotenuse has a length of $208$, what is the length of the side adjacent to the $52°$ angle (to the nearest whole number)?

Which of the following statements is true about the angle formed by two perpendicular lines in a right triangle?

In which right triangle is the value of $x$ equal to ${\cos }^{-1}\left(\frac{4.3}{6.7}\right)$?

Given a right triangle where angle $\mathrm{BAC}$ is one of the acute angles, what is the degree measure of angle $\mathrm{BAC}$? Round your answer to the nearest whole degree.

A circle has a radius of $10$ inches and a central angle of $3\mathrm{rad}$. What is the approximate length of the arc $s$ subtended by this angle? Choose the closest value.

Concept Check Suppose that ―90° < θ < 90° .   Find the sign of each function value. sec θ/2