Solve the following triangle, rounding all approximated values to the nearest hundredth: 72.1° 4
Solve the following triangle, rounding all approximated values to the nearest hundredth: 72.1° 4
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°.
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Concept explainers
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
![### Solving a Right Triangle
To solve the following right triangle, round all approximated values to the nearest hundredth:
#### Diagram Description
- The triangle is a right triangle.
- The base (adjacent side to the angle) is labeled as 4 units.
- The angle adjacent to the base is 72.1 degrees.
- The opposite side is labeled as \( x \).
- The hypotenuse is labeled as \( y \).
- The other angle opposite the base is labeled as \( z \).
#### Steps for Solving:
1. **Finding \( x \)**:
\[ x = \tan(72.1^\circ) \cdot 4 \]
Calculation:
\[ \tan(72.1^\circ) \approx 3.077 \]
\[ x \approx 3.077 \cdot 4 \approx 12.31 \]
2. **Finding \( y \)**:
\[ y = \frac{4}{\cos(72.1^\circ)} \]
Calculation:
\[ \cos(72.1^\circ) \approx 0.309 \]
\[ y \approx \frac{4}{0.309} \approx 12.94 \]
3. **Finding \( z \)**:
Since the sum of angles in any triangle is 180° and one angle is 90°:
\[ z = 90^\circ - 72.1^\circ \approx 17.9^\circ \]
### Summary of Results:
- \( x \approx 12.31 \)
- \( y \approx 12.94 \)
- \( z \approx 17.9^\circ \)
By following these steps, you can solve the given right triangle, rounding all values to the nearest hundredth as required.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd24861ef-92b0-4cd8-8c54-2ac2200498ec%2Ff28071c1-d86d-4aa9-8983-164fb9e6fd30%2F912c7na_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving a Right Triangle
To solve the following right triangle, round all approximated values to the nearest hundredth:
#### Diagram Description
- The triangle is a right triangle.
- The base (adjacent side to the angle) is labeled as 4 units.
- The angle adjacent to the base is 72.1 degrees.
- The opposite side is labeled as \( x \).
- The hypotenuse is labeled as \( y \).
- The other angle opposite the base is labeled as \( z \).
#### Steps for Solving:
1. **Finding \( x \)**:
\[ x = \tan(72.1^\circ) \cdot 4 \]
Calculation:
\[ \tan(72.1^\circ) \approx 3.077 \]
\[ x \approx 3.077 \cdot 4 \approx 12.31 \]
2. **Finding \( y \)**:
\[ y = \frac{4}{\cos(72.1^\circ)} \]
Calculation:
\[ \cos(72.1^\circ) \approx 0.309 \]
\[ y \approx \frac{4}{0.309} \approx 12.94 \]
3. **Finding \( z \)**:
Since the sum of angles in any triangle is 180° and one angle is 90°:
\[ z = 90^\circ - 72.1^\circ \approx 17.9^\circ \]
### Summary of Results:
- \( x \approx 12.31 \)
- \( y \approx 12.94 \)
- \( z \approx 17.9^\circ \)
By following these steps, you can solve the given right triangle, rounding all values to the nearest hundredth as required.
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