Geometry

Question Analysis

The main focus is to apply the Pythagorean Theorem to find the length of the unknown leg  in the given right - triangle. We need to identify the lengths of the hypotenuse and the other leg and substitute them into the theorem.

 

Key Concept Explanation

The Pythagorean Theorem states that for a right - triangle with legs of lengths  and  and hypotenuse of length , the equation is . When we know the hypotenuse  and one leg , and want to find the other leg , we can rearrange the formula as .

 

Step - by - Step Solution

1. Identify the sides of the right - triangle:

The hypotenuse  and one leg , and the unknown leg is .

2. Apply the Pythagorean Theorem:

Substitute the values into the formula .

First, calculate

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