Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Solve the Law of Cosines: [tex]c^2 = a^2 + b^2 - 2ab \cos C[/tex] for [tex]\cos C[/tex].

A. [tex]\cos C = \frac{a^2 + b^2 - c^2}{2ab}[/tex]
B. [tex]\cos C = \frac{a^2 + b^2 + c^2}{-2ab}[/tex]
C. [tex]\cos C = \frac{c^2 - a^2 - b^2}{2ab}[/tex]
D. [tex]\cos C = \frac{-c^2 + a^2 + b^2}{-2ab}[/tex]

Sagot :

GinnyAnswer
To solve for \(\cos C\) using the Law of Cosines, we start with the given equation:

[tex]\[ c^2 = a^2 + b^2 - 2ab \cos C \][/tex]

We need to isolate \(\cos C\). Here are the steps to do so:

1. Start with the equation:
[tex]\[ c^2 = a^2 + b^2 - 2ab \cos C \][/tex]

2. Rearrange the equation to isolate the term involving \(\cos C\). Subtract \(a^2 + b^2\) from both sides:
[tex]\[ c^2 - a^2 - b^2 = -2ab \cos C \][/tex]

3. Divide both sides of the equation by \(-2ab\) to solve for \(\cos C\):
[tex]\[ \cos C = \frac{c^2 - a^2 - b^2}{-2ab} \][/tex]

4. Simplify the equation by factoring out a negative sign in the numerator:
[tex]\[ \cos C = \frac{-(a^2 + b^2 - c^2)}{2ab} \][/tex]

5. Rearranging the terms in the numerator gives:
[tex]\[ \cos C = \frac{a^2 + b^2 - c^2}{2ab} \][/tex]

Therefore, the correct expression for \(\cos C\) is:
[tex]\[ \cos C = \frac{a^2 + b^2 - c^2}{2ab} \][/tex]

Thus, the correct choice from the given options is:
[tex]\[ \cos C = \frac{a^2 + b^2 - c^2}{2ab} \][/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.