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Ch. 1 - Trigonometric Functions
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. 1 - Trigonometric FunctionsProblem 32
Chapter 2, Problem 32

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

Verified step by step guidance
1
Recall that complementary angles are two angles whose measures add up to 90 degrees. So, if the two angles are \(3x - 5\) and \(6x - 40\), their sum is \(90\) degrees.
Set up the equation representing the sum of the complementary angles: \[(3x - 5) + (6x - 40) = 90\]
Combine like terms on the left side: \[3x + 6x - 5 - 40 = 90\] which simplifies to \[9x - 45 = 90\]
Solve for \(x\) by first adding 45 to both sides: \[9x = 90 + 45\] then divide both sides by 9: \[x = \frac{135}{9}\]
Once you find the value of \(x\), substitute it back into the expressions for each angle: \[3x - 5\] and \[6x - 40\] to find their measures.

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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.
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Intro to Complementary & Supplementary Angles

Algebraic Expressions in Angle Measures

Angles can be represented using algebraic expressions involving variables. To find the actual angle measures, you need to form and solve equations based on these expressions, applying algebraic techniques such as combining like terms and isolating variables.
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Simplifying Trig Expressions

Solving Linear Equations

Solving for the variable in the angle expressions requires knowledge of linear equations. This involves manipulating the equation formed by the sum of the angles to find the value of the variable, which can then be substituted back to find each angle's measure.
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Solving Linear Equations
Related Practice
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.) IV , x/y

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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)

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

178Β°

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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

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