Solve the triangle, if possible. a = 26.38 km, b= 21.64 km, c = 18.31 km Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Round to the nearest hundredth as needed.) OA. There are two possible solutions for the triangle. The measurements for the solution with smaller angle A are as follows. A B C≈ The measurements for the solution with larger angle A are as follows. A B C≈ OB. There is only one possible solution for the triangle. The measurements for angles A, B, and C are as follows. A≈ Ba C≈ OC. There are no possible solutions for this triangle.
Solve the triangle, if possible. a = 26.38 km, b= 21.64 km, c = 18.31 km Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Round to the nearest hundredth as needed.) OA. There are two possible solutions for the triangle. The measurements for the solution with smaller angle A are as follows. A B C≈ The measurements for the solution with larger angle A are as follows. A B C≈ OB. There is only one possible solution for the triangle. The measurements for angles A, B, and C are as follows. A≈ Ba C≈ OC. There are no possible solutions for this triangle.
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
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Chapter23: Basic Calculations Of Percentages, Percents, And Rates
Section: Chapter Questions
Problem 5A: The length, L, of the standard 82° included angle drill can be calculated using the formula L=0.575...
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![**Solve the Triangle, if Possible**
Given:
\[ a = 26.38 \, \text{km}, \, b = 21.64 \, \text{km}, \, c = 18.31 \, \text{km} \]
**Instruction:**
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Round to the nearest hundredth as needed.)
1. **Option A:** There are two possible solutions for the triangle.
- The measurements for the solution with smaller angle \( A \) are as follows:
\[ A \approx \, \_\_\_\_^\circ \]
\[ B \approx \, \_\_\_\_^\circ \]
\[ C \approx \, \_\_\_\_^\circ \]
- The measurements for the solution with the larger angle \( A \) are as follows:
\[ A \approx \, \_\_\_\_^\circ \]
\[ B \approx \, \_\_\_\_^\circ \]
\[ C \approx \, \_\_\_\_^\circ \]
2. **Option B:** There is only one possible solution for the triangle.
- The measurements for angles \( A \), \( B \), and \( C \) are as follows:
\[ A \approx \, \_\_\_\_^\circ \]
\[ B \approx \, \_\_\_\_^\circ \]
\[ C \approx \, \_\_\_\_^\circ \]
3. **Option C:** There are no possible solutions for this triangle.
**Explanation:**
Triangles can be solved using the given three sides (a, b, c). The goal is to determine the angles (A, B, C) that correspond to these sides. There are different potential cases:
- **Two possible solutions (Option A):** This occurs in an ambiguous case, typically when given two sides and a non-included angle (SSA condition).
- **One possible solution (Option B):** This occurs in determinate conditions, such as SSS (side-side-side) or SAS (side-angle-side).
- **No possible solution (Option C):** Such as when the given dimensions do not satisfy the triangle inequality theorem (sum of any two sides must be greater than the remaining side).
**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96f2e08c-aa5d-4493-8570-9d5ecf302bf0%2F57ee5e8c-8770-4deb-a58b-12472f55665e%2F3hkqt57_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve the Triangle, if Possible**
Given:
\[ a = 26.38 \, \text{km}, \, b = 21.64 \, \text{km}, \, c = 18.31 \, \text{km} \]
**Instruction:**
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Round to the nearest hundredth as needed.)
1. **Option A:** There are two possible solutions for the triangle.
- The measurements for the solution with smaller angle \( A \) are as follows:
\[ A \approx \, \_\_\_\_^\circ \]
\[ B \approx \, \_\_\_\_^\circ \]
\[ C \approx \, \_\_\_\_^\circ \]
- The measurements for the solution with the larger angle \( A \) are as follows:
\[ A \approx \, \_\_\_\_^\circ \]
\[ B \approx \, \_\_\_\_^\circ \]
\[ C \approx \, \_\_\_\_^\circ \]
2. **Option B:** There is only one possible solution for the triangle.
- The measurements for angles \( A \), \( B \), and \( C \) are as follows:
\[ A \approx \, \_\_\_\_^\circ \]
\[ B \approx \, \_\_\_\_^\circ \]
\[ C \approx \, \_\_\_\_^\circ \]
3. **Option C:** There are no possible solutions for this triangle.
**Explanation:**
Triangles can be solved using the given three sides (a, b, c). The goal is to determine the angles (A, B, C) that correspond to these sides. There are different potential cases:
- **Two possible solutions (Option A):** This occurs in an ambiguous case, typically when given two sides and a non-included angle (SSA condition).
- **One possible solution (Option B):** This occurs in determinate conditions, such as SSS (side-side-side) or SAS (side-angle-side).
- **No possible solution (Option C):** Such as when the given dimensions do not satisfy the triangle inequality theorem (sum of any two sides must be greater than the remaining side).
**
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