Domanda del libro di testo
In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
3v - 4w
797
views
Ch. 4 - Laws of Sines and Cosines; Vectors
Blitzer3rd EditionTrigonometryISBN: 9780137316601
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
Capitolo 4, Problema 34
In Exercises 33–38, find the area of the triangle having the given measurements. Round to the nearest square unit.
A = 22°, b = 20 feet, c = 50 feet
Guida verificata passo dopo passo1
Identify the given elements of the triangle: angle \(A = 22^\circ\), side \(b = 20\) feet, and side \(c = 50\) feet. We need to find the area of the triangle.
Recall the formula for the area of a triangle when two sides and the included angle are known: \(\text{Area} = \frac{1}{2}bc \sin A\).
Substitute the known values into the formula: \(\text{Area} = \frac{1}{2} \times 20 \times 50 \times \sin 22^\circ\).
Calculate \(\sin 22^\circ\) using a calculator or trigonometric table to find the sine of the angle.
Multiply the values together to find the area, then round the result to the nearest whole number as requested.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Law of Cosines
The Law of Cosines relates the lengths of sides of a triangle to the cosine of one of its angles. It is useful for finding unknown sides or angles in any triangle, especially when two sides and the included angle are known. The formula is c² = a² + b² - 2ab cos(C).
Video consigliato:
Percorso guidato
4:35
Intro to Law of Cosines
Area of a Triangle Using Two Sides and Included Angle
The area of a triangle can be calculated using two sides and the included angle with the formula: Area = 1/2 * b * c * sin(A). This method is efficient when two sides and the angle between them are given, avoiding the need to find the third side.
Video consigliato:
Percorso guidato
4:02Calculating Area of SAS Triangles
Trigonometric Functions and Angle Measurement
Understanding sine and cosine functions and how to apply them to angles measured in degrees is essential. These functions relate angles to ratios of sides in right triangles and are fundamental in solving oblique triangles and calculating areas.
Video consigliato:
Percorso guidato
6:04Introduction to Trigonometric Functions
Pratica correlata
Domanda del libro di testo
In Exercises 35–36, the three given points are the vertices of a triangle. Solve each triangle, rounding lengths of sides to the nearest tenth and angle measures to the nearest degree.
A(0, 0), B(-3, 4), C(3, -1)
718
views
Domanda del libro di testo
In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively.
a = 1.4, b = 2.9, A = 142°
1073
views
Domanda del libro di testo
In Exercises 33–38, find projᵥᵥ v. Then decompose v into two vectors, v₁ and v₂, where v₁ is parallel to w and v₂ is orthogonal to w. v = 3i - 2j, w = i - j
769
views
Domanda del libro di testo
In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
||2u||
772
views
Domanda del libro di testo
In Exercises 33–38, find projᵥᵥ v. Then decompose v into two vectors, v₁ and v₂, where v₁ is parallel to w and v₂ is orthogonal to w.
v = i + 3j, w = -2i + 5j
646
views