---# Calculating the Length of a Right Triangle's LegTo 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 unitsUsing 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.---

We have to find the unknown leg length. Pythagoras theorem says that,…

Answered: What is the unknown leg length?…

Math

Algebra

What is the unknown leg length? Pythagorean theorem:a2+b2=c2 122+b2 = 152 %3D 144 +b2 = 225 b2 = 81 %3D b = cm

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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