Textbook Question
Fill in the blank(s) to correctly complete each sentence.
An equilateral triangle has _________________ equal sides.
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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 1
Fill in the blank(s) to correctly complete each sentence.
The sum of the measures of the angles of any triangle is ________________ .
Verified step by step guidance1
Recall the fundamental property of triangles in Euclidean geometry: the sum of the interior angles of any triangle is always the same.
This property states that when you add up the measures of all three interior angles of a triangle, the total is a constant value.
Express this property mathematically as: \(\angle A + \angle B + \angle C = 180^\circ\), where \(\angle A\), \(\angle B\), and \(\angle C\) are the measures of the three angles of the triangle.
Understand that this is true for all types of triangles, whether they are acute, obtuse, or right triangles.
Therefore, the blank should be filled with the value that represents this constant sum, which is \(180^\circ\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Triangle Angle Sum Theorem
This theorem states that the sum of the interior angles of any triangle is always 180 degrees. It is a fundamental property used to solve for unknown angles in triangles.
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Solving Right Triangles with the Pythagorean Theorem
Interior Angles of a Triangle
Interior angles are the angles inside a triangle formed by its sides. Understanding that these three angles together add up to a fixed total helps in solving various geometric and trigonometric problems.
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Basic Angle Measurement
Angles are measured in degrees or radians, with degrees being common in basic geometry. Knowing how to measure and add angles is essential for applying the triangle angle sum property correctly.
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5:31Reference Angles on the Unit Circle
Related Practice
Textbook Question
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. Given tan θ = 1/cot θ , two equivalent forms of this identity are cot θ = 1/______ and tan θ . ______ = 1 .
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Textbook Question
CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. One degree, written 1°, represents ____________ of a complete rotation.
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Textbook Question
Fill in the blank(s) to correctly complete each sentence.
An isosceles right triangle has one ________________ angle and ______________ equal sides.
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Textbook Question
Give the measures of the complement and the supplement of an angle measuring 35° .
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