5 dicals as needed.)
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
**Diagram Explanation:**
The provided diagram is a right triangle with one side labeled as 5, the hypotenuse labeled as 11, and the other side left unknown.
### Instructions:
Find the exact length of the unknown side and provide your answer both as an exact value (using radicals if necessary) and as a decimal rounded to two decimal places.
---
**Answer Section:**
The exact answer is: \[ \square \]
*(Simplify your answer. Type an exact answer using radicals as needed.)*
### Solution Steps:
1. Label the triangle sides:
- \(a = 5\) (leg)
- \(c = 11\) (hypotenuse)
- \(b\) unknown (other leg)
2. Apply the Pythagorean theorem:
\[a^2 + b^2 = c^2\]
3. Plug in the known values:
\[5^2 + b^2 = 11^2\]
4. Simplify:
\[25 + b^2 = 121\]
5. Isolate \(b^2\):
\[b^2 = 121 - 25\]
\[b^2 = 96\]
6. Solve for \(b\):
\[b = \sqrt{96}\]
7. Simplify the radical (if necessary) and provide the exact value:
\[b = 4\sqrt{6}\]
8. Calculate the decimal approximation:
\[b \approx 9.80\]
---
**Final Answer:**
- Exact answer: \[ 4\sqrt{6} \]
- Decimal approximation (two-decimal places): \[ 9.80 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b70f989-f4fe-4180-9465-a46932af6785%2F1b428fc4-92db-4cc8-8501-8567f538b0f1%2F4hp07rm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Application of the Pythagorean Theorem
Use the Pythagorean theorem to find the unknown side of the right triangle. Provide both an exact answer and a two-decimal-place approximation.
**Diagram Explanation:**
The provided diagram is a right triangle with one side labeled as 5, the hypotenuse labeled as 11, and the other side left unknown.
### Instructions:
Find the exact length of the unknown side and provide your answer both as an exact value (using radicals if necessary) and as a decimal rounded to two decimal places.
---
**Answer Section:**
The exact answer is: \[ \square \]
*(Simplify your answer. Type an exact answer using radicals as needed.)*
### Solution Steps:
1. Label the triangle sides:
- \(a = 5\) (leg)
- \(c = 11\) (hypotenuse)
- \(b\) unknown (other leg)
2. Apply the Pythagorean theorem:
\[a^2 + b^2 = c^2\]
3. Plug in the known values:
\[5^2 + b^2 = 11^2\]
4. Simplify:
\[25 + b^2 = 121\]
5. Isolate \(b^2\):
\[b^2 = 121 - 25\]
\[b^2 = 96\]
6. Solve for \(b\):
\[b = \sqrt{96}\]
7. Simplify the radical (if necessary) and provide the exact value:
\[b = 4\sqrt{6}\]
8. Calculate the decimal approximation:
\[b \approx 9.80\]
---
**Final Answer:**
- Exact answer: \[ 4\sqrt{6} \]
- Decimal approximation (two-decimal places): \[ 9.80 \]
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