2. Trigonometric Functions on Right Triangles

A right triangle has a base of $68$ units and the angle opposite the height is $15°$. What is the height of the triangle?

Triangle xyz was transformed by a dilation with center O and scale factor $3$. If the original length of side xy was $1.5$ units, what is the length of side xy after the transformation?

Triangle QRS is a right triangle with angle Q equal to $90°$ and angle R equal to $35°$. What is the measure of the obtuse angle in triangle QRS?

In a right triangle $FGH$, if the length of $FH$ is $18$ units and angle $G$ is $30°$, what is the length of side $FG$ opposite angle $H$?

A right triangle with an angle of $31°$ has a hypotenuse of $10$. Calculate the side of the triangle opposite to the $31°$ angle (y), and the side adjacent to the $31°$ angle (x). Round your answer to 3 decimal places.

Given the right triangle below, calculate all missing angles in degrees (round your answer to 3 decimal places.

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).

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).

Graph one period of each function. y = 2 tan x/2

Graph two periods of the given tangent function. y = 3 tan x/4

Graph two periods of the given tangent function. y = −2 tan (1/2) x

Graph two periods of the given tangent function. y = tan(x − π/4)

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

In Exercises 55–58, use a graph to solve each equation for -2π ≤ x ≤ 2π. tan x = -1