Textbook Question
Find the unknown side lengths in each pair of similar triangles.
Ch. 1 - Trigonometric Functions
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 2, Problem 22
Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 50° 40' 50"
Verified step by step guidance1
Understand the definitions: The complement of an angle is what, when added to the angle, equals 90 degrees, and the supplement of an angle is what, when added to the angle, equals 180 degrees.
Convert the given angle 50° 40' 50" into a consistent format if needed, but since the problem is in degrees, minutes, and seconds, we can work directly with these units.
To find the complement, subtract the given angle from 90° 0' 0" using the subtraction of degrees, minutes, and seconds carefully:
\[ \text{Complement} = 90^\circ 0' 0'' - 50^\circ 40' 50'' \]
To find the supplement, subtract the given angle from 180° 0' 0" similarly:
\[ \text{Supplement} = 180^\circ 0' 0'' - 50^\circ 40' 50'' \]
Perform the subtraction step-by-step, borrowing minutes and seconds as necessary to handle the subtraction of minutes and seconds correctly.
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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°. This concept is essential for problems involving right angles and angle pairs.
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Intro to Complementary & Supplementary Angles
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°. This concept is important when dealing with straight lines and linear pairs of angles.
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3:35Intro to Complementary & Supplementary Angles
Angle Measurement in Degrees, Minutes, and Seconds
Angles can be measured in degrees (°), minutes ('), and seconds ("). One degree equals 60 minutes, and one minute equals 60 seconds. Properly converting and subtracting these units is crucial when calculating complements and supplements of angles given in this format.
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5:31Reference Angles on the Unit Circle
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
In each figure, there are two similar triangles. Find the unknown measurement. Give any approximation to the nearest tenth.
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Textbook Question
Length of a Shadow If a tree 20 ft tall casts a shadow 8 ft long, how long would the shadow of a 30-ft tree be at the same time and place?
Textbook Question
Find the measure of each marked angle. See Example 2.
Textbook Question
The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 37° , 52°