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,...
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# Calculating the Length of a Right Triangle's Leg
To determine the length of an unknown leg in a right triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) is one leg of the triangle,
- \( b \) is the other leg of the triangle,
- \( c \) is the hypotenuse of the triangle.
### Example Problem:
**What is the unknown leg length?**
Given:
- One leg (\( a \)) = 12 units
- Hypotenuse (\( c \)) = 15 units
Using the Pythagorean theorem:
\[ 12^2 + b^2 = 15^2 \]
First, calculate the squares:
\[ 144 + b^2 = 225 \]
Now, solve for \( b^2 \):
\[ b^2 = 225 - 144 \]
\[ b^2 = 81 \]
Finally, take the square root to find \( b \):
\[ b = \sqrt{81} \]
\[ b = 9 \]
**Therefore, the unknown leg length is 9 units.**
---
### Diagram/Graph Explanation:
There is no diagram or graph in the provided image. The educational content is focused on the step-by-step algebraic solution of finding the unknown leg of a right triangle using the Pythagorean theorem.
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Transcribed Image Text:---
# Calculating the Length of a Right Triangle's Leg
To determine the length of an unknown leg in a right triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) is one leg of the triangle,
- \( b \) is the other leg of the triangle,
- \( c \) is the hypotenuse of the triangle.
### Example Problem:
**What is the unknown leg length?**
Given:
- One leg (\( a \)) = 12 units
- Hypotenuse (\( c \)) = 15 units
Using the Pythagorean theorem:
\[ 12^2 + b^2 = 15^2 \]
First, calculate the squares:
\[ 144 + b^2 = 225 \]
Now, solve for \( b^2 \):
\[ b^2 = 225 - 144 \]
\[ b^2 = 81 \]
Finally, take the square root to find \( b \):
\[ b = \sqrt{81} \]
\[ b = 9 \]
**Therefore, the unknown leg length is 9 units.**
---
### Diagram/Graph Explanation:
There is no diagram or graph in the provided image. The educational content is focused on the step-by-step algebraic solution of finding the unknown leg of a right triangle using the Pythagorean theorem.
---
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