C b 88° В A
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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.
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