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 39

Capitolo 3, Problema 39

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. B = 39°09', c = 0.6231 m

Guida verificata passo dopo passo

Identify the given elements of the right triangle: angle \( B = 39^\circ 09' \) and side \( c = 0.6231 \) meters, where \( c \) is the hypotenuse since angle \( C = 90^\circ \).

Use the fact that the sum of angles in a triangle is \( 180^\circ \). Since \( C = 90^\circ \), find angle \( A \) by calculating \( A = 90^\circ - B \). Remember to subtract the minutes properly when working with degrees and minutes.

Apply the sine and cosine definitions to find the other two sides: \( a = c \times \sin(B) \) and \( b = c \times \cos(B) \). Convert angle \( B \) from degrees and minutes to decimal degrees if necessary for calculation, then convert back to degrees and minutes for the final answer if required.

Calculate side \( a \) using \( a = c \times \sin(B) \) and side \( b \) using \( b = c \times \cos(B) \), keeping units consistent.

Summarize the solution by listing all sides \( a, b, c \) and angles \( A, B, C \) with angles expressed in degrees and minutes as requested.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Right Triangle Properties

A right triangle has one angle equal to 90°, and the other two angles sum to 90°. Knowing one acute angle and a side allows the use of trigonometric ratios to find unknown sides and angles. The right angle simplifies calculations by providing a fixed reference.

Video consigliato:

Percorso guidato

5:35

30-60-90 Triangles

Trigonometric Ratios and Functions

Sine, cosine, and tangent relate the angles of a right triangle to the ratios of its sides. For example, sine of an angle equals the opposite side over the hypotenuse. These ratios help solve for unknown sides or angles when partial information is given.

Video consigliato:

Percorso guidato

6:04

Introduction to Trigonometric Functions

Angle Measurement and Conversion

Angles can be expressed in degrees and minutes or decimal degrees. Understanding how to convert between these formats is essential for accurate calculations and final answers, especially when the problem specifies a particular format for reporting results.

Video consigliato:

Percorso guidato

5:31

Reference Angles on the Unit Circle

Pratica correlata

Domanda del libro di testo

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. cos(2θ + 50°) = sin(2θ - 20°)

585

views

Domanda del libro di testo

Find the exact value of each expression. See Example 3. sin 1305°

635

views

Domanda del libro di testo

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. sec(3β + 10°) = csc(β + 8°)

726

views

Domanda del libro di testo

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. csc(β + 40°) = sec(β - 20°)

618

views

Domanda del libro di testo

Find the exact value of each expression. See Example 3. tan(-1020°)

597

views

Domanda del libro di testo

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. A = 53°24', c = 387.1 ft

581

views