Questions: For the right triangle below, find the length of (x). Round to the nearest hundredth (two decimal places).

Transcript text: For the right triangle below, find the length of $x$. \[ x= \] Round to the nearest hundredth (two decimal places).

Solution

Solution Steps

Step 1: Identify the given sides of the right triangle

We are given a right triangle with legs of length 8 and 13, and a hypotenuse of length $x$.

Step 2: Apply the Pythagorean theorem

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (called legs). In this case, we have: $x^2 = 8^2 + 13^2$

Step 3: Calculate the squares of the lengths of the legs

$8^2 = 64$ $13^2 = 169$

Step 4: Add the squares of the legs

$x^2 = 64 + 169$ $x^2 = 233$

Step 5: Find the square root to solve for x

$x = \sqrt{233}$ $x \approx 15.26$