Ch. 1 - Trigonometric Functions

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. 1 - Trigonometric Functions

Problem 31

Chapter 2, Problem 31

Find the measure of each marked angle. See Example 2 complementary angles with measures 9𝓍 + 6 and 3𝓍 degrees

Verified step by step guidance

Recall that complementary angles are two angles whose measures add up to 90 degrees. So, set up the equation: $ (9x + 6) + 3x = 90 $.

Combine like terms on the left side of the equation: $ 9x + 6 + 3x = 90 $ becomes $ 12x + 6 = 90 $.

Isolate the variable term by subtracting 6 from both sides: $ 12x = 90 - 6 $ which simplifies to $ 12x = 84 $.

Solve for $x$ by dividing both sides by 12: $ x = \frac{84}{12} $.

Once you find $x$, substitute it back into the expressions for the angles $9x + 6$ and \$3x$ to find the measure of each marked angle.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. Understanding this relationship allows you to set up an equation where the sum of the given angle expressions equals 90, which is essential for solving for the variable.

Algebraic Expressions in Angle Measures

Angles can be represented using algebraic expressions involving variables. To find the actual angle measures, you need to translate the problem into an equation and solve for the variable, then substitute back to find each angle's measure.

Solving Linear Equations

Solving for the variable requires knowledge of linear equations. You combine like terms, isolate the variable, and solve the equation to find its value, which then helps determine the numerical values of the angles.

Recommended video:

7:48

Solving Linear Equations

Related Practice

Textbook Question

Find the measure of each marked angle. See Example 2 complementary angles with measures 3𝓍 ― 5 and 6𝓍 ― 40 degrees

Textbook Question

Find the values of the six trigonometric functions for an angle in standard position having each given point on its terminal side. Rationalize denominators when applicable. (6√3 , ―6)

views

Textbook Question

Find the measure of the smaller angle formed by the hands of a clock at the following times.

views

Textbook Question

Sketch an angle θ in standard position such that θ has the least positive measure, and the given point is on the terminal side of θ. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. See Examples 1, 2, and 4. (―2√3 , 2)

views

Textbook Question

Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2.

178°

views

Textbook Question

Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = √(x² + y²) .(Hint: Drawing a sketch may help.) III , y/r

views