Skip to main content
Ch. 7 - Applications of Trigonometry and Vectors
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 7 - Applications of Trigonometry and VectorsProblema 35
Capitolo 8, Problema 35

Solve each triangle. See Examples 2 and 3.


a = 3.0 ft, b = 5.0 ft, c = 6.0 ft

Guida verificata passo dopo passo
1
Identify the given sides of the triangle: \(a = 3.0\) ft, \(b = 5.0\) ft, and \(c = 6.0\) ft. Since all three sides are known, this is a side-side-side (SSS) triangle problem.
Use the Law of Cosines to find one of the angles. For example, to find angle \(C\) opposite side \(c\), use the formula: \[\cos C = \frac{a^2 + b^2 - c^2}{2ab}\]
Calculate \(\cos C\) by substituting the known side lengths into the formula, then find angle \(C\) by taking the inverse cosine (arccos) of that value: \[C = \cos^{-1}\left(\frac{a^2 + b^2 - c^2}{2ab}\right)\]
Repeat the Law of Cosines to find another angle, for example angle \(B\) opposite side $b\(, using: \[\cos B = \frac{a^2 + c^2 - b^2}{2ac}\] and then find \)B = \cos^{-1}(\text{value})$.
Find the third angle \(A\) using the fact that the sum of angles in a triangle is \(180^\circ\): \[A = 180^\circ - B - C\].

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.

Law of Cosines

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is especially useful for solving triangles when all three sides are known, allowing calculation of each angle using the formula: c² = a² + b² - 2ab·cos(C).
Video consigliato:
Percorso guidato
4:35
Intro to Law of Cosines

Triangle Classification and Properties

Understanding the types of triangles (acute, obtuse, or right) based on side lengths helps in interpreting results. The triangle inequality theorem ensures the given sides can form a triangle, and recognizing side relationships aids in predicting angle sizes.
Video consigliato:
Percorso guidato
4:42
Review of Triangles

Angle Sum Property of Triangles

The sum of the interior angles in any triangle is always 180 degrees. After finding two angles using the Law of Cosines, the third angle can be found by subtracting their sum from 180°, completing the solution of the triangle.
Video consigliato:
Percorso guidato
4:47
Sum and Difference of Tangent
Pratica correlata
Domanda del libro di testo

A ship is sailing due north. At a certain point the bearing of a lighthouse 12.5 km away is N 38.8° E. Later on, the captain notices that the bearing of the lighthouse has become S 44.2° E. How far did the ship travel between the two observations of the lighthouse?

1369
views
Domanda del libro di testo

Two forces of 128 lb and 253 lb act on a point. The resultant force is 320 lb. Find the angle between the forces.

849
views
Domanda del libro di testo

A force of 28.7 lb makes an angle of 42° 10′ with a second force. The resultant of the two forces makes an angle of 32° 40′ with the first force. Find the magnitudes of the second force and of the resultant.


<IMAGE>

794
views
Domanda del libro di testo

Apply the law of sines to the following:


A = 104°, a = 26.8, b = 31.3.


What happens when we try to find the measure of angle B using a calculator?

719
views
Domanda del libro di testo

Radio direction finders are placed at points A and B, which are 3.46 mi apart on an east-west line, with A west of B. From A the bearing of a certain radio transmitter is 47.7°, and from B the bearing is 302.5°. Find the distance of the transmitter from A.

913
views
Domanda del libro di testo

A force of 176 lb makes an angle of 78° 50′ with a second force. The resultant of the two forces makes an angle of 41° 10′ with the first force. Find the magnitudes of the second force and of the resultant.


<IMAGE>

924
views