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 4
Capitolo 8, Problema 4

CONCEPT PREVIEW Assume a triangle ABC has standard labeling.


a. Determine whether SAA, ASA, SSA, SAS, or SSS is given.


b. Determine whether the law of sines or the law of cosines should be used to begin solving the triangle.


a, B, and C

Guida verificata passo dopo passo
1
Step 1: Identify the given parts of the triangle. The problem states that sides and angles given are 'a', 'B', and 'C'. Here, 'a' is the side opposite angle 'A', and 'B' and 'C' are two angles of the triangle.
Step 2: Determine the type of information given. Since two angles (B and C) and one side (a) are known, this corresponds to the SSA (Side-Side-Angle) case, because you have one side and two angles, but the side is not between the two known angles.
Step 3: Recall the criteria for each case: SAA (two angles and a non-included side), ASA (two angles and the included side), SSA (two sides and a non-included angle), SAS (two sides and the included angle), and SSS (three sides). Since you have two angles and one side opposite an unknown angle, this is SSA.
Step 4: Decide which law to use. The Law of Sines is typically used when you have an angle-side opposite pair and another angle or side, which fits the SSA case here.
Step 5: Conclude that to begin solving the triangle with given 'a', 'B', and 'C', you should use the Law of Sines, which is given by the formula: \(\frac{a}{\sin\left( A \right)} = \frac{b}{\sin\left( B \right)} = \frac{c}{\sin\left( C \right)}\).

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.

Triangle Congruence and Similarity Criteria

Triangle congruence criteria such as SAA (or AAS), ASA, SSA, SAS, and SSS describe specific combinations of sides and angles that determine a unique triangle. Understanding these helps identify what information is given and what methods apply for solving the triangle.
Video consigliato:
Percorso guidato
5:35
30-60-90 Triangles

Law of Sines

The Law of Sines relates the ratios of sides to the sines of their opposite angles in any triangle. It is especially useful when two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA) are known, allowing for the determination of unknown sides or angles.
Video consigliato:
Percorso guidato
4:27
Intro to Law of Sines

Law of Cosines

The Law of Cosines generalizes the Pythagorean theorem for any triangle, relating the lengths of sides to the cosine of an included angle. It is typically used when two sides and the included angle (SAS) or all three sides (SSS) are known, enabling calculation of unknown sides or angles.
Video consigliato:
Percorso guidato
4:35
Intro to Law of Cosines
Pratica correlata
Domanda del libro di testo

In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?

c. no triangle

<IMAGE>

614
views
Domanda del libro di testo

Determine the number of triangles ABC possible with the given parts.


a = 50, b = 26, A = 95°

1040
views
Domanda del libro di testo

Use the law of sines to find the indicated part of each triangle ABC.


Find b if a = 165 m, A = 100.2°, B = 25.0°

736
views
Domanda del libro di testo

CONCEPT PREVIEW Refer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.



-b

560
views
Domanda del libro di testo

In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?

a. two triangles

<IMAGE>

817
views
Domanda del libro di testo

In each figure, a line segment of length L is to be drawn from the given point to the positive x-axis in order to form a triangle. For what value(s) of L can we draw the following?

b. exactly one triangle

<IMAGE>

592
views