Solve the triangle, if possible. 16 15 A 24

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°.
icon
Related questions
Question
**Solve the Triangle**

To solve the triangle, if possible.

**Diagram Explanation:**

The image depicts a triangle labeled as follows:

- **Points:** A, B, and C
- **Sides:** 
  - AB = 24 units
  - AC = 16 units
  - BC = 15 units

**Steps to Solve the Triangle:**

1. **Verify if it is a Right Triangle:**  
   Use the Pythagorean theorem \( a^2 + b^2 = c^2 \) to determine if the triangle is right-angled.
   - Here, the longest side is 24 (hypotenuse if right-angled).
   - Check: \( 16^2 + 15^2 = 256 + 225 = 481 \)
   - \( 24^2 = 576 \)
   - Since \( 481 \neq 576 \), this is not a right triangle.

2. **Use the Law of Cosines to find angles:**  
   To find angle \( A \):
   \[
   \cos A = \frac{b^2 + c^2 - a^2}{2bc} 
   \]
   Substituting the respective values:
   \[
   \cos A = \frac{16^2 + 15^2 - 24^2}{2 \times 16 \times 15}
   \]

3. **Solve for other angles and sides if needed:**
   Use the solved angle to find the remaining angles using the Law of Sines or by once again applying the Law of Cosines.

**Note:**
After solving angles or additional sides, verify the triangle's properties based on calculations.
Transcribed Image Text:**Solve the Triangle** To solve the triangle, if possible. **Diagram Explanation:** The image depicts a triangle labeled as follows: - **Points:** A, B, and C - **Sides:** - AB = 24 units - AC = 16 units - BC = 15 units **Steps to Solve the Triangle:** 1. **Verify if it is a Right Triangle:** Use the Pythagorean theorem \( a^2 + b^2 = c^2 \) to determine if the triangle is right-angled. - Here, the longest side is 24 (hypotenuse if right-angled). - Check: \( 16^2 + 15^2 = 256 + 225 = 481 \) - \( 24^2 = 576 \) - Since \( 481 \neq 576 \), this is not a right triangle. 2. **Use the Law of Cosines to find angles:** To find angle \( A \): \[ \cos A = \frac{b^2 + c^2 - a^2}{2bc} \] Substituting the respective values: \[ \cos A = \frac{16^2 + 15^2 - 24^2}{2 \times 16 \times 15} \] 3. **Solve for other angles and sides if needed:** Use the solved angle to find the remaining angles using the Law of Sines or by once again applying the Law of Cosines. **Note:** After solving angles or additional sides, verify the triangle's properties based on calculations.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Law of Cosines
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry
Algebra and Trigonometry
Trigonometry
ISBN:
9781938168376
Author:
Jay Abramson
Publisher:
OpenStax
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning