Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
100%
![**Problem: Find the Unknown Length in a Right Triangle**
You are given a right triangle with the following measurements:
- One leg is 11 cm.
- The hypotenuse is 15 cm.
- The other leg is unknown (?).
**Question:**
The unknown length is approximately ____ cm.
(Type an integer or decimal rounded to the nearest thousandth as needed.)
To solve this problem, you can use the Pythagorean theorem which states that in a right-angled triangle:
\[ a^2 + b^2 = c^2 \]
where:
- \(a\) and \(b\) are the lengths of the legs
- \(c\) is the length of the hypotenuse
Let's denote:
- The known leg as \(a = 11 \) cm.
- The hypotenuse as \(c = 15\) cm.
- The unknown leg as \(b\).
Plugging in the known values into the Pythagorean theorem:
\[ 11^2 + b^2 = 15^2 \]
\[ 121 + b^2 = 225 \]
Subtracting 121 from both sides:
\[ b^2 = 225 - 121 \]
\[ b^2 = 104 \]
Taking the square root of both sides:
\[ b = \sqrt{104} \]
\[ b \approx 10.198 \]
So, the unknown length is approximately **10.198 cm**.
Make sure you round the final answer to the nearest thousandth as indicated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5da6b72-6f0b-4b5b-b99e-129f8d660be8%2F0cd22be6-4eb6-441d-91df-0b3d3dfcc8f3%2Fbe9tjyqo_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Find the Unknown Length in a Right Triangle**
You are given a right triangle with the following measurements:
- One leg is 11 cm.
- The hypotenuse is 15 cm.
- The other leg is unknown (?).
**Question:**
The unknown length is approximately ____ cm.
(Type an integer or decimal rounded to the nearest thousandth as needed.)
To solve this problem, you can use the Pythagorean theorem which states that in a right-angled triangle:
\[ a^2 + b^2 = c^2 \]
where:
- \(a\) and \(b\) are the lengths of the legs
- \(c\) is the length of the hypotenuse
Let's denote:
- The known leg as \(a = 11 \) cm.
- The hypotenuse as \(c = 15\) cm.
- The unknown leg as \(b\).
Plugging in the known values into the Pythagorean theorem:
\[ 11^2 + b^2 = 15^2 \]
\[ 121 + b^2 = 225 \]
Subtracting 121 from both sides:
\[ b^2 = 225 - 121 \]
\[ b^2 = 104 \]
Taking the square root of both sides:
\[ b = \sqrt{104} \]
\[ b \approx 10.198 \]
So, the unknown length is approximately **10.198 cm**.
Make sure you round the final answer to the nearest thousandth as indicated.
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 3 steps with 3 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education