4. Problem 7.1.32 b А. 44.4°, 44.4°, 91.2° В. 20.5°, 20.5°, 139.0° С. 45°, 45°, 90° D. 45.6°, 45.6°, 88.8° Е. 69.5°, 69.5°, 41.0°
4. Problem 7.1.32 b А. 44.4°, 44.4°, 91.2° В. 20.5°, 20.5°, 139.0° С. 45°, 45°, 90° D. 45.6°, 45.6°, 88.8° Е. 69.5°, 69.5°, 41.0°
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°.
Related questions
Question
Find the indicated measure, to the nearest
tenth.
you are allowed to use a calculator. there is only one answer.
Transcribed Image Text:## Question 4: Problem 7.1.32 b
Choose the correct set of angles for the given problem.
**Options:**
- **A.** 44.4°, 44.4°, 91.2°
- **B.** 20.5°, 20.5°, 139.0°
- **C.** 45°, 45°, 90°
- **D.** 45.6°, 45.6°, 88.8°
- **E.** 69.5°, 69.5°, 41.0°
*Note*: This problem involves selecting the appropriate set of angles, possibly for a geometrical figure or trigonometric problem, based on the given criteria or context.
![**Question 32:** An isosceles triangle has sides measuring 10 inches, 7 inches, and 7 inches. What are the measures of its angles?
**Solution:**
To find the angles of the isosceles triangle:
1. **Identify the Sides:**
The triangle has two equal sides measuring 7 inches each, and a base measuring 10 inches.
2. **Use the Cosine Rule:**
To find one of the base angles (let's denote it as \( A \)), we use:
\[
\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}
\]
where \( a = 10 \), \( b = 7 \), \( c = 7 \).
3. **Calculate:**
\[
\cos(A) = \frac{7^2 + 7^2 - 10^2}{2 \times 7 \times 7} = \frac{49 + 49 - 100}{98} = \frac{-2}{98} = -\frac{1}{49}
\]
\[
A = \cos^{-1}\left(-\frac{1}{49}\right)
\]
4. **Find Angles:**
- Two angles are equal since it is an isosceles triangle, so angle \( B = A \).
- The third angle \( C \) at the base is:
\[
C = 180^\circ - 2A
\]
By calculating with a calculator, you can find the precise measures of the angles as decimals.
**Conclusion:**
The base angles \( A \) and \( B \) are approximately equal, and the third angle \( C \) completes the triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdaa77415-d220-4776-9d7c-d055c20faba9%2F2ad740e1-b63a-46ee-9910-15c4bea6947b%2Fug62n6_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 32:** An isosceles triangle has sides measuring 10 inches, 7 inches, and 7 inches. What are the measures of its angles?
**Solution:**
To find the angles of the isosceles triangle:
1. **Identify the Sides:**
The triangle has two equal sides measuring 7 inches each, and a base measuring 10 inches.
2. **Use the Cosine Rule:**
To find one of the base angles (let's denote it as \( A \)), we use:
\[
\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}
\]
where \( a = 10 \), \( b = 7 \), \( c = 7 \).
3. **Calculate:**
\[
\cos(A) = \frac{7^2 + 7^2 - 10^2}{2 \times 7 \times 7} = \frac{49 + 49 - 100}{98} = \frac{-2}{98} = -\frac{1}{49}
\]
\[
A = \cos^{-1}\left(-\frac{1}{49}\right)
\]
4. **Find Angles:**
- Two angles are equal since it is an isosceles triangle, so angle \( B = A \).
- The third angle \( C \) at the base is:
\[
C = 180^\circ - 2A
\]
By calculating with a calculator, you can find the precise measures of the angles as decimals.
**Conclusion:**
The base angles \( A \) and \( B \) are approximately equal, and the third angle \( C \) completes the triangle.
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