Domanda del libro di testo
Solve each triangle. See Examples 2 and 3.
a = 3.0 ft, b = 5.0 ft, c = 6.0 ft
676
views
Ch. 7 - Applications of Trigonometry and Vectors
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- 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
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 8, Problema 34
Two forces of 128 lb and 253 lb act on a point. The resultant force is 320 lb. Find the angle between the forces.
Guida verificata passo dopo passo1
Identify the given quantities: two forces with magnitudes \(F_1 = 128\) lb and \(F_2 = 253\) lb, and their resultant force \(R = 320\) lb. We need to find the angle \(\theta\) between these two forces.
Recall the law of cosines for vectors, which relates the magnitudes of two vectors and their resultant:
\(R^2 = F_1^2 + F_2^2 + 2 F_1 F_2 \cos(\theta)\)
Substitute the known values into the equation:
\(320^2 = 128^2 + 253^2 + 2 \times 128 \times 253 \times \cos(\theta)\)
Rearrange the equation to isolate \(\cos(\theta)\):
\(\cos(\theta) = \frac{320^2 - 128^2 - 253^2}{2 \times 128 \times 253}\)
Calculate the right-hand side value (without final numeric evaluation here), then use the inverse cosine function to find the angle:
\(\theta = \cos^{-1}(\text{value from previous step})\)
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.
Resultant of Two Forces
The resultant force is the single force that has the same effect as the two given forces acting together. It can be found using vector addition, considering both magnitude and direction of the forces.
Video consigliato:
Percorso guidato
5:28
Equations with Two Variables
Law of Cosines in Vector Addition
The law of cosines relates the magnitudes of two vectors and the angle between them to the magnitude of their resultant. It is expressed as R² = A² + B² - 2AB cos(θ), where θ is the angle between the forces.
Video consigliato:
Percorso guidato
4:35Intro to Law of Cosines
Solving for the Angle Between Forces
By rearranging the law of cosines formula, the angle between two forces can be found using θ = cos⁻¹((A² + B² - R²) / (2AB)). This allows determination of the angle when the magnitudes and resultant are known.
Video consigliato:
Percorso guidato
04:33Find the Angle Between Vectors
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
Given u = 〈-2, 5〉 and v = 〈4, 3〉, find each of the following.
v - u
723
views
Domanda del libro di testo
To determine the distance RS across a deep canyon, Rhonda lays off a distance TR = 582 yd. She then finds that T = 32° 50' and R = 102° 20'. Find RS. See the figure.
<IMAGE>
727
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
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