Questions: For the following right triangle, find the side length x. Round your answer to the nearest hundredth.

For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
Transcript text: For the following right triangle, find the side length $x$. Round your answer to the nearest hundredth.
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Solution

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Solution Steps

Step 1: Identify the given values

We are given a right triangle with the hypotenuse \( c = 25 \) and one leg \( b = 15 \). We need to find the length of the other leg \( x \).

Step 2: Apply the Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the legs and \( c \) is the hypotenuse.

Step 3: Substitute the known values into the equation

Substitute \( b = 15 \) and \( c = 25 \) into the equation: \[ x^2 + 15^2 = 25^2 \]

Step 4: Simplify the equation

Calculate the squares: \[ x^2 + 225 = 625 \]

Step 5: Solve for \( x^2 \)

Subtract 225 from both sides: \[ x^2 = 625 - 225 \] \[ x^2 = 400 \]

Step 6: Find \( x \)

Take the square root of both sides: \[ x = \sqrt{400} \] \[ x = 20 \]

Final Answer

The length of the side \( x \) is \( 20.00 \) (rounded to the nearest hundredth).

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