2. Trigonometric Functions on Right Triangles

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.

If the vertex angle of an isosceles triangle is $110°$, what is the measure of each base angle?

Solve each problem.See Examples 3 and 4. Angle of Elevation of the Sun The length of the shadow of a building 34.09 m tall is 37.62 m. Find the angle of elevation of the sun to the nearest hundredth of a degree.

In a right triangle, one leg measures $8\mathrm{cm}$ and the hypotenuse measures $16\mathrm{cm}$. What is the length of the other leg?

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

If a right triangle has one angle measuring $30°$, what is the measure of the other non-right angle?

Solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. a = 10.8, b = 24.7

In Exercises 29–36, find the length x to the nearest whole unit.

Solve each right triangle. When two sides are given, give angles in degrees and minutes.

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

Given a right triangle where one leg has length $6$, the other leg has length $8$, and the hypotenuse is $x$, what is the value of $x$?

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 29–36, find the length x to the nearest whole unit.

Solve each problem. See Examples 1–4. Distance across a Lake To find the distance RS across a lake, a surveyor lays off length RT = 53.1 m, so that angle T = 32°10' and angle S = 57°50'. Find length RS.

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