der the triangle shown below where m/B = 76°, a = 35.6 cm, and c = 32.1 cm.
Mathematics For Machine Technology
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ISBN:9781337798310
Author:Peterson, John.
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Chapter87: An Introduction To G- And M-codes For Cnc Programming
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Problem 23A: Write a G-code program for the counterclockwise arc with starting point (-40, -20), ending point...
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In the triangle, the vertices are labeled as follows:
- \(A\)
- \(B\)
- \(C\)
The sides are represented as:
- \(AB = 32.1 \text{ cm}\)
- \(BC = 35.6 \text{ cm}\)
- \(AC = x \text{ cm}\)
The angle given is \(\angle B = 76^\circ\).
**Objective:** Use the Law of Cosines to determine the value of \( x \) (the length of \( AC \) in cm).
The Law of Cosines states:
\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]
We need to re-arrange the formula to solve for \( x \):
\[ x^2 = a^2 + c^2 - 2ac \cdot \cos(B) \]
Given,
\( a = 35.6 \text{ cm} \),
\( c = 32.1 \text{ cm} \),
\( \angle B = 76^\circ \),
Plug these values into the formula to find \( x \).
```markdown
x = [input box]
[Preview button]
```](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F370a7c6f-923c-4e3e-b2e2-de29038e74c7%2F900434b0-ee21-4ae0-8482-008973297794%2Fqr9kd3_processed.png&w=3840&q=75)
Transcribed Image Text:### Solving for x using the Law of Cosines
Consider the triangle shown below where \( m\angle B = 76^\circ \), \( a = 35.6 \text{ cm} \), and \( c = 32.1 \text{ cm} \).
In the triangle, the vertices are labeled as follows:
- \(A\)
- \(B\)
- \(C\)
The sides are represented as:
- \(AB = 32.1 \text{ cm}\)
- \(BC = 35.6 \text{ cm}\)
- \(AC = x \text{ cm}\)
The angle given is \(\angle B = 76^\circ\).
**Objective:** Use the Law of Cosines to determine the value of \( x \) (the length of \( AC \) in cm).
The Law of Cosines states:
\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]
We need to re-arrange the formula to solve for \( x \):
\[ x^2 = a^2 + c^2 - 2ac \cdot \cos(B) \]
Given,
\( a = 35.6 \text{ cm} \),
\( c = 32.1 \text{ cm} \),
\( \angle B = 76^\circ \),
Plug these values into the formula to find \( x \).
```markdown
x = [input box]
[Preview button]
```
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