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
Question
![### Solving the Right Triangle
Below are two diagrams of right triangles that we need to solve.
#### Triangle 1:
This is a right triangle labeled with vertices A, B, and C. The right angle is at vertex C.
- **Side AC (hypotenuse):** 14 units
- **Side BC (opposite):** 10 units
- **Side AB (adjacent):** (It is not labeled and needs to be solved)
To solve for side AB, we use the Pythagorean Theorem:
\[ a^2 + b^2 = c^2 \]
Here, \( c = 14 \), \( b = 10 \):
\[ AB^2 + 10^2 = 14^2 \]
\[ AB^2 + 100 = 196 \]
\[ AB^2 = 96 \]
\[ AB = \sqrt{96} = 4 \sqrt{6} \approx 9.8 \text{ units} \]
#### Triangle 2:
This triangle is also labeled with vertices A, B, and C. The right angle is at vertex B.
- **Side AB (hypotenuse):** (It is not labeled and needs to be solved)
- **Side BC (opposite):** 16 units
- **Side AC (adjacent):** (It is not labeled and needs to be solved)
To solve for the sides AB and AC, we again use the Pythagorean Theorem:
Let's assume AC = \( a \) and AB = \( c \):
From the right triangle relationship:
\[ c^2 = 16^2 + a^2 \]
\[ c^2 = 256 + a^2 \]
Without additional information, if we are given the length of side AC or the length of side AB, we can substitute back to solve for the missing side.
### Conclusion:
Solving for the unknowns in right triangles involves using the Pythagorean Theorem to determine the length of the missing side given information about the other two sides. This method is essential for solving various problems involving right triangles in geometry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f6f557d-9e1e-46fd-a63e-879d74571691%2F6856fd53-e9d2-403e-ba0f-3c285e6346fa%2Fgk6br5p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving the Right Triangle
Below are two diagrams of right triangles that we need to solve.
#### Triangle 1:
This is a right triangle labeled with vertices A, B, and C. The right angle is at vertex C.
- **Side AC (hypotenuse):** 14 units
- **Side BC (opposite):** 10 units
- **Side AB (adjacent):** (It is not labeled and needs to be solved)
To solve for side AB, we use the Pythagorean Theorem:
\[ a^2 + b^2 = c^2 \]
Here, \( c = 14 \), \( b = 10 \):
\[ AB^2 + 10^2 = 14^2 \]
\[ AB^2 + 100 = 196 \]
\[ AB^2 = 96 \]
\[ AB = \sqrt{96} = 4 \sqrt{6} \approx 9.8 \text{ units} \]
#### Triangle 2:
This triangle is also labeled with vertices A, B, and C. The right angle is at vertex B.
- **Side AB (hypotenuse):** (It is not labeled and needs to be solved)
- **Side BC (opposite):** 16 units
- **Side AC (adjacent):** (It is not labeled and needs to be solved)
To solve for the sides AB and AC, we again use the Pythagorean Theorem:
Let's assume AC = \( a \) and AB = \( c \):
From the right triangle relationship:
\[ c^2 = 16^2 + a^2 \]
\[ c^2 = 256 + a^2 \]
Without additional information, if we are given the length of side AC or the length of side AB, we can substitute back to solve for the missing side.
### Conclusion:
Solving for the unknowns in right triangles involves using the Pythagorean Theorem to determine the length of the missing side given information about the other two sides. This method is essential for solving various problems involving right triangles in geometry.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
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