Ch. 1 - Trigonometric Functions

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

Lial 12th Edition

Ch. 1 - Trigonometric Functions

Problem 18

Chapter 2, Problem 18

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 89°

Verified step by step guidance

Understand the definitions: The complement of an angle is what, when added to the angle, equals 90°. The supplement of an angle is what, when added to the angle, equals 180°.

To find the complement of the given angle (89°), set up the equation: \(\text{complement} + 89^\circ = 90^\circ\).

Solve for the complement by subtracting 89° from 90°: \(\text{complement} = 90^\circ - 89^\circ\).

To find the supplement of the given angle (89°), set up the equation: \(\text{supplement} + 89^\circ = 180^\circ\).

Solve for the supplement by subtracting 89° from 180°: \(\text{supplement} = 180^\circ - 89^\circ\).

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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. To find the complement of a given angle, subtract the angle's measure from 90°. For example, the complement of 30° is 60° because 30° + 60° = 90°.

Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees. To find the supplement of a given angle, subtract the angle's measure from 180°. For instance, the supplement of 110° is 70° since 110° + 70° = 180°.

Angle Measurement and Units

Angles are measured in degrees, representing the amount of rotation between two rays. Understanding how to interpret and manipulate angle measures is essential for solving problems involving complements and supplements, especially when working with degrees.

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Related Practice

Textbook Question

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

Textbook Question

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

Textbook Question

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 14° 20'

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Textbook Question

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1.

sin θ , given that csc θ = √24/3

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Textbook Question

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1. cot θ , given that tan θ = 18

Textbook Question

Find all unknown angle measures in each pair of similar triangles.