Domanda del libro di testo
Find the angle between each pair of vectors. Round to two decimal places as necessary.
3i + 4j, j
623
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 59
A painter is going to apply paint to a triangular metal plate on a new building. Two sides measure 16.1 m and 15.2 m, and the angle between the sides is 125°. What is the area of the surface to be painted?
Guida verificata passo dopo passo1
Identify the formula for the area of a triangle when two sides and the included angle are known: \( \text{Area} = \frac{1}{2}ab\sin(C) \), where \( a \) and \( b \) are the sides, and \( C \) is the included angle.
Substitute the given values into the formula: \( a = 16.1 \), \( b = 15.2 \), and \( C = 125^\circ \).
Calculate the sine of the angle: \( \sin(125^\circ) \).
Multiply the values: \( \frac{1}{2} \times 16.1 \times 15.2 \times \sin(125^\circ) \).
The result from the multiplication will give you the area of the triangular metal plate in square meters.
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 for Area Calculation
The area of a triangle can be found using two sides and the included angle with the formula: Area = 1/2 * a * b * sin(C). This method is useful when the height is unknown but two sides and the angle between them are given.
Video consigliato:
Percorso guidato
4:30
Calculating Area of ASA Triangles
Sine Function in Trigonometry
The sine of an angle in a triangle relates the angle to the ratio of the opposite side over the hypotenuse in a right triangle. In this context, sine helps calculate the height component needed to find the area when using the formula involving two sides and the included angle.
Video consigliato:
Percorso guidato
6:04Introduction to Trigonometric Functions
Triangle Area Calculation
The area of a triangle is generally calculated as half the product of its base and height. When height is not directly known, trigonometric functions like sine allow us to find the effective height using given sides and angles.
Video consigliato:
Percorso guidato
4:30Calculating Area of ASA Triangles
Pratica correlata
Domanda del libro di testo
Find the angle between each pair of vectors. Round to two decimal places as necessary.
〈1, 6〉, 〈-1, 7〉
543
views
Domanda del libro di testo
A plane is headed due south with an airspeed of 192 mph. A wind from a direction of 78.0° is blowing at 23.0 mph. Find the ground speed and resulting bearing of the plane.
784
views
Domanda del libro di testo
Find the area of each triangle ABC.
A = 59.80°, b = 15.00 cm, C = 53.10°
676
views
Domanda del libro di testo
Find the angle between each pair of vectors. Round to two decimal places as necessary.
〈4, 0〉, 〈2, 2〉
609
views
Domanda del libro di testo
A real estate agent wants to find the area of a triangular lot. A surveyor takes measurements and finds that two sides are 52.1 m and 21.3 m, and the angle between them is 42.2°. What is the area of the triangular lot?
761
views