Use the Law of Cosines to solve for the largest angle in the triangle with the given measures. Round answers to the nearest hundredth. a = 38 m, b= 10 m, c = 31 m 3 OA= 108.65° A = 128.15° B=129.3° B= 101.3°
Use the Law of Cosines to solve for the largest angle in the triangle with the given measures. Round answers to the nearest hundredth. a = 38 m, b= 10 m, c = 31 m 3 OA= 108.65° A = 128.15° B=129.3° B= 101.3°
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Using the Law of Cosines in Triangle Calculations
#### Problem Statement:
Use the Law of Cosines to solve for the largest angle in the triangle with the given measurements. Round answers to the nearest hundredth.
Given:
- \(a = 38 \text{ m}\)
- \(b = 10 \text{ m}\)
- \(c = 31 \text{ m}\)
#### Solution Options:
- \( \circ \ A = 108.65^\circ \)
- \( \circ \ A = 128.15^\circ \)
- \( \circ \ B = 129.3^\circ \)
- \( \circ \ B = 101.3^\circ \)
To determine the largest angle in a triangle with given side lengths, we apply the Law of Cosines which states:
\[
\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}
\]
Here, to find the angle, we rearrange the equation:
\[
C = \cos^{-1} \left( \frac{a^2 + b^2 - c^2}{2ab} \right)
\]
Calculating each step accurately is essential to finding the correct angle measurement and solving the problem accordingly. In this scenario, you should compute each angle to determine which one corresponds to the largest angle based on the given side lengths.
Use this format to proceed with the needed calculations.
---
Feel free to visit our Educational Resources section to find more comprehensive guides and examples on the application of the Law of Cosines, as well as interactive practice problems to solidify your understanding!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febfa71ca-f003-4e76-b16d-d56ed3281ebe%2Fb72b4a55-92f8-4a2b-9d31-05d3c6f76e28%2Fq8iwfx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Using the Law of Cosines in Triangle Calculations
#### Problem Statement:
Use the Law of Cosines to solve for the largest angle in the triangle with the given measurements. Round answers to the nearest hundredth.
Given:
- \(a = 38 \text{ m}\)
- \(b = 10 \text{ m}\)
- \(c = 31 \text{ m}\)
#### Solution Options:
- \( \circ \ A = 108.65^\circ \)
- \( \circ \ A = 128.15^\circ \)
- \( \circ \ B = 129.3^\circ \)
- \( \circ \ B = 101.3^\circ \)
To determine the largest angle in a triangle with given side lengths, we apply the Law of Cosines which states:
\[
\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}
\]
Here, to find the angle, we rearrange the equation:
\[
C = \cos^{-1} \left( \frac{a^2 + b^2 - c^2}{2ab} \right)
\]
Calculating each step accurately is essential to finding the correct angle measurement and solving the problem accordingly. In this scenario, you should compute each angle to determine which one corresponds to the largest angle based on the given side lengths.
Use this format to proceed with the needed calculations.
---
Feel free to visit our Educational Resources section to find more comprehensive guides and examples on the application of the Law of Cosines, as well as interactive practice problems to solidify your understanding!
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