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 other leg and the hypotenuse 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 . We can rearrange this formula to find the length of a leg when the hypotenuse and the other leg are known.

 

Step - by - Step Solution

1. Identify the sides of the right - triangle:

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

2. Apply the Pythagorean Theorem:

Starting with , we can rearrange it to solve for  (where  is ): .

Substitute

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