Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![The image depicts a right triangle labeled \(\triangle STU\). Here is a detailed description for educational purposes:
1. **Triangle Description**:
- The triangle is labeled with vertices \( S \) (top vertex), \( T \) (bottom left vertex), and \( U \) (bottom right vertex).
- There is a right angle at vertex \( S \), which is indicated by a red square at that corner.
- The angle at vertex \( T \) is marked as \( 42^\circ \).
- The length of the side \( TU \) is given as \( 9.5 \) inches.
2. **Question**:
- Find the length of the side \( ST \).
3. **Diagram Explanation**:
- The triangle \( STU \) is a right triangle where the hypotenuse \( TU \) measures \( 9.5 \) inches.
- The \( 42^\circ \) angle at vertex \( T \) provides a clue to use trigonometric functions to find the unknown lengths of the sides.
To solve this problem, trigonometric ratios can be used, particularly:
\[ \sin(\theta) \]
\[ \cos(\theta) \]
\[ \tan(\theta) \]
With \( \theta = 42^\circ \) and the hypotenuse known:
\[ \cos(42^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{ST}{TU} \]
Solve for \( ST \):
\[ ST = TU \times \cos(42^\circ) \]
Given \( TU = 9.5 \) inches, we have:
\[ ST = 9.5 \times \cos(42^\circ) \]
Use a calculator to find \( \cos(42^\circ) \):
\[ \cos(42^\circ) \approx 0.7431 \]
Now calculate \( ST \):
\[ ST \approx 9.5 \times 0.7431 \approx 7.06 \text{ inches} \]
So the length of \( ST \) is approximately \( 7.06 \) inches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc48d8489-347d-4dda-adf7-92ca178e6f4b%2Ff51b3151-73ce-4a9a-8456-2c1d87c75a48%2Fow32vk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image depicts a right triangle labeled \(\triangle STU\). Here is a detailed description for educational purposes:
1. **Triangle Description**:
- The triangle is labeled with vertices \( S \) (top vertex), \( T \) (bottom left vertex), and \( U \) (bottom right vertex).
- There is a right angle at vertex \( S \), which is indicated by a red square at that corner.
- The angle at vertex \( T \) is marked as \( 42^\circ \).
- The length of the side \( TU \) is given as \( 9.5 \) inches.
2. **Question**:
- Find the length of the side \( ST \).
3. **Diagram Explanation**:
- The triangle \( STU \) is a right triangle where the hypotenuse \( TU \) measures \( 9.5 \) inches.
- The \( 42^\circ \) angle at vertex \( T \) provides a clue to use trigonometric functions to find the unknown lengths of the sides.
To solve this problem, trigonometric ratios can be used, particularly:
\[ \sin(\theta) \]
\[ \cos(\theta) \]
\[ \tan(\theta) \]
With \( \theta = 42^\circ \) and the hypotenuse known:
\[ \cos(42^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{ST}{TU} \]
Solve for \( ST \):
\[ ST = TU \times \cos(42^\circ) \]
Given \( TU = 9.5 \) inches, we have:
\[ ST = 9.5 \times \cos(42^\circ) \]
Use a calculator to find \( \cos(42^\circ) \):
\[ \cos(42^\circ) \approx 0.7431 \]
Now calculate \( ST \):
\[ ST \approx 9.5 \times 0.7431 \approx 7.06 \text{ inches} \]
So the length of \( ST \) is approximately \( 7.06 \) inches.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning