Ch. 2 - Acute Angles and Right Triangles

Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo

Lial 12th Edition

Ch. 2 - Acute Angles and Right Triangles

Problema 14

Capitolo 3, Problema 14

Solve each right triangle. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2.

Guida verificata passo dopo passo

Identify the given sides of the right triangle. Label the sides as opposite (O), adjacent (A), and hypotenuse (H) relative to the angle you want to find.

Use the Pythagorean theorem \(H^2 = O^2 + A^2\) to find the missing side if only two sides are given and the hypotenuse is not one of them.

Apply the appropriate trigonometric ratio to find the unknown angles. For example, use \(\sin \theta = \frac{O}{H}\), \(\cos \theta = \frac{A}{H}\), or \(\tan \theta = \frac{O}{A}\) depending on the sides you have.

Calculate the angle in degrees using the inverse trigonometric function, such as \(\theta = \sin^{-1}\left(\frac{O}{H}\right)\), \(\theta = \cos^{-1}\left(\frac{A}{H}\right)\), or \(\theta = \tan^{-1}\left(\frac{O}{A}\right)\).

Convert the decimal degrees to degrees and minutes by separating the integer part as degrees and multiplying the decimal part by 60 to get minutes.

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Pythagorean Theorem

The Pythagorean theorem relates the lengths of the sides in a right triangle: the square of the hypotenuse equals the sum of the squares of the other two sides. It is essential for finding the missing side when two sides are known.

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Solving Right Triangles with the Pythagorean Theorem

Trigonometric Ratios (Sine, Cosine, Tangent)

Sine, cosine, and tangent ratios connect the angles of a right triangle to the ratios of its sides. These ratios allow calculation of unknown angles or sides when two sides are given, using inverse trigonometric functions for angle determination.

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Sine, Cosine, & Tangent of 30°, 45°, & 60°

Angle Measurement in Degrees and Minutes

Angles can be expressed in degrees and minutes, where one degree equals 60 minutes. Converting decimal degrees to degrees and minutes is important for precise angle representation, especially in practical applications like navigation or surveying.

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Percorso guidato

5:31

Reference Angles on the Unit Circle

Pratica correlata

Domanda del libro di testo

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Use the Pythagorean theorem to find the unknown side length. Then find exact values of the six trigonometric functions for angle B. Rationalize denominators when applicable. See Example 1. b = 8, c = 11

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Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1. I. II. 5. A. 45° 6. B. 60° 7. C. 82° 8. D. 30° 9. E. 38° 10. 480° F. 32°

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Find exact values of the six trigonometric functions for each angle. Do not use a calculator. Rationalize denominators when applicable. 120°

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Domanda del libro di testo

Solve each right triangle. When two sides are given, give angles in degrees and minutes.

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