Final answer:
To find the side labeled x, we can use the Pythagorean theorem to relate the lengths of the sides of a right triangle. By substituting the known side lengths into the equation and solving for x, we can find its value. The answer is approximately 12.00000.
Step-by-step explanation:
The question asks us to find the side labeled x. In order to determine the relationship between x and the other sides of the triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In equation form, this can be written as:
a² + b² = c²
where a and b are the lengths of the legs and c is the length of the hypotenuse.
Since we are looking for the side labeled x, we can replace a and b with the known side lengths and solve for x:
x² + 5² = 13²
Simplifying the equation gives:
x² + 25 = 169
Subtracting 25 from both sides of the equation gives:
x² = 144
Taking the square root of both sides gives:
x = √144
Rounding to 5 decimal places, the value of x is approximately 12.00000.