Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles39m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

1. Measuring Angles

Angles in Standard Position

Trigonometry

1. Measuring Angles

Angles in Standard Position

1:24 minutes

Problem 4a

Textbook Question

In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 87.177°

Verified step by step guidance

Understand the classification of angles: Acute angles are less than 90°, right angles are exactly 90°, obtuse angles are greater than 90° but less than 180°, and straight angles are exactly 180°.

Identify the given angle measure: 87.177°.

Compare the given angle measure to the classifications: Check if 87.177° is less than 90°, equal to 90°, greater than 90° but less than 180°, or equal to 180°.

Determine the classification based on the comparison: Since 87.177° is less than 90°, it falls into the category of acute angles.

Conclude that the angle is classified as an acute angle.

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Key Concepts

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

Types of Angles

Angles can be classified into four main types based on their measures: acute angles (less than 90°), right angles (exactly 90°), obtuse angles (greater than 90° but less than 180°), and straight angles (exactly 180°). Understanding these classifications is essential for determining the nature of any given angle.

Angle Measurement

Angles are measured in degrees, with a full rotation around a point equating to 360°. The measurement of an angle helps in identifying its classification. For example, an angle measuring 87.177° is less than 90°, indicating it is acute.

Visual Representation of Angles

Visualizing angles can aid in their classification. Drawing angles or using protractors can help students see the differences between acute, right, obtuse, and straight angles. This visual approach reinforces understanding and assists in accurately categorizing angles based on their measures.