2. Trigonometric Functions on Right Triangles

In Exercises 49–54, find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the nearest whole number.

In a right triangle, one leg has length $5$ and the other leg has length $12$. What is the approximate degree measure of the angle opposite the leg of length $5$?

In a right triangle, if one leg has length $3$ units, the other leg has length $4$ units, what is the length of the side opposite the right angle (the hypotenuse)?

In a right triangle, one leg has length $6$ and the other leg has length $8$. What is the length of the hypotenuse?

In a right triangle, if one leg has length $3$ units, the other leg has length $4$ units, and angle $b$ is opposite the side of unknown length, what is the length of the side opposite angle $b$?

In parallelogram LMNO, if angle L measures $35°$, what is the measure of angle O?

Given a right triangle with one leg measuring $15$cm, how many distinct right triangles (up to congruence) can be constructed with this information alone?

Given two parallel lines cut by a transversal, if one of the alternate interior angles measures $k$ degrees and the other measures $71$ degrees, what is the value of $k$?

In a right triangle, one leg has length $6$ units and the hypotenuse has length $10$ units. What is the length of the other leg?

The graph of a tangent function is given. Select the equation for each graph from the following options: y = tan(x + π/2), y = tan(x + π), y = -tan x, y = −tan(x − π/2).

In right triangle $ABC$, angle $B$ is the right angle. If $AB$ = $7$ units and $BC$ = $9$ units, what is the length of line segment $AC$?

Given a right triangle where one leg has length $5$ units and the other leg has length $12$ units, what is the length of the hypotenuse? Round your answer to the nearest hundredth.

In a right triangle, one leg has length $6$ and the other leg has length $8$. What is the length of the hypotenuse $x$? Select the correct answer.

Given a right triangle with an angle $\theta$ and an adjacent side of length $a$, and hypotenuse of length $c$, which equation finds the value of $\theta$?

Given right triangle xyz, if angle x is $30°$ and the length of the side opposite angle x is $5$, what is the length of the hypotenuse?