Domanda del libro di testo
Fill in the blank(s) to correctly complete each sentence.
A triangle that is not a right triangle is a(n) _________ triangle.
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Ch. 7 - Applications of Trigonometry and Vectors
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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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 3
Use the law of sines to find the indicated part of each triangle ABC.
Find B if C = 51.3°, c = 68.3 m, b = 58.2 m
Guida verificata passo dopo passo1
Identify the known parts of the triangle: angle \(C = 51.3^\circ\), side \(c = 68.3\) m (opposite angle \(C\)), and side \(b = 58.2\) m (opposite angle \(B\)). We need to find angle \(B\).
Recall the Law of Sines formula: \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\). We will use the relationship between sides \(b\), \(c\) and angles \(B\), \(C\).
Set up the equation using the Law of Sines for sides \(b\) and \(c\): \(\frac{b}{\sin B} = \frac{c}{\sin C}\). Substitute the known values: \(\frac{58.2}{\sin B} = \frac{68.3}{\sin 51.3^\circ}\).
Solve for \(\sin B\) by cross-multiplying: \(\sin B = \frac{58.2 \times \sin 51.3^\circ}{68.3}\). Calculate the right side to find \(\sin B\) (do not compute the final value here).
Find angle \(B\) by taking the inverse sine (arcsin) of the value obtained for \(\sin B\): \(B = \sin^{-1}(\sin B)\). Remember to consider the possible ambiguous case for angle \(B\) in the triangle.
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Concetti chiave
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Law of Sines
The Law of Sines relates the ratios of the lengths of sides of a triangle to the sines of their opposite angles. It states that (a/sin A) = (b/sin B) = (c/sin C). This law is useful for solving triangles when given two angles and one side or two sides and a non-included angle.
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Percorso guidato
4:27
Intro to Law of Sines
Triangle Angle Sum Property
The sum of the interior angles in any triangle is always 180°. Knowing two angles allows you to find the third by subtracting their sum from 180°. This property helps verify or find missing angles after applying the Law of Sines.
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Percorso guidato
4:47Sum and Difference of Tangent
Solving for an Unknown Angle
When two sides and an angle opposite one of them are known, the Law of Sines can be used to find an unknown angle by rearranging the formula and using inverse sine functions. Care must be taken to consider the ambiguous case where two different angles may satisfy the equation.
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Percorso guidato
2:28Solving Problems with Complementary & Supplementary Angles
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
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Domanda del libro di testo
Use the law of sines to find the indicated part of each triangle ABC.
Find b if C = 74.2°, c = 96.3 m, B = 39.5
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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>
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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>
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Domanda del libro di testo
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
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