C b 88° В A
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter7: Equations And Inequalities In Two Variables
Section7.3: Distance And Slope
Problem 13PS
Related questions
Question
Use the Law of Cosines to determine the indicated side x. (Assume b = 8 and c = 2. Round your answer to one decimal place.)
x=
![The diagram represents a triangle labeled ABC. The angle at vertex A is given as 88°. The side opposing this angle is labeled "x." The other two sides are labeled "b" and "c" respectively. Specifically:
- Side "b" is between vertices A and C.
- Side "c" is between vertices A and B.
- Side "x" is between vertices B and C.
This geometric configuration can be used to instruct students on various concepts of trigonometry such as the Law of Sines or Law of Cosines, both of which rely on the lengths of sides and measures of angles within a triangle.
1. **Understanding Triangle Properties**:
- The sum of the angles in a triangle is always 180°.
- Given one angle, one can often compute others, especially if additional sides or angles are known.
2. **Law of Sines**:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
Used when we know either two angles and one side or two sides and a non-included angle.
3. **Law of Cosines**:
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
This can be specifically useful here given the value of one angle is stated, and if we have further lengths of sides, other lengths or angles can be calculated.
This diagram serves as an informative visual aid to explain these principles in further detail.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb62fb42d-f2b4-4330-85ad-951614f13399%2Fff1b2a11-cfd9-432a-9d40-a612ccc01ccd%2Fm4oklj5.gif&w=3840&q=75)
Transcribed Image Text:The diagram represents a triangle labeled ABC. The angle at vertex A is given as 88°. The side opposing this angle is labeled "x." The other two sides are labeled "b" and "c" respectively. Specifically:
- Side "b" is between vertices A and C.
- Side "c" is between vertices A and B.
- Side "x" is between vertices B and C.
This geometric configuration can be used to instruct students on various concepts of trigonometry such as the Law of Sines or Law of Cosines, both of which rely on the lengths of sides and measures of angles within a triangle.
1. **Understanding Triangle Properties**:
- The sum of the angles in a triangle is always 180°.
- Given one angle, one can often compute others, especially if additional sides or angles are known.
2. **Law of Sines**:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
Used when we know either two angles and one side or two sides and a non-included angle.
3. **Law of Cosines**:
\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]
This can be specifically useful here given the value of one angle is stated, and if we have further lengths of sides, other lengths or angles can be calculated.
This diagram serves as an informative visual aid to explain these principles in further detail.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
