Answer: The missing side length is approximately 11.54.
Step-by-step explanation: To find the missing side length using the Pythagorean theorem, we need to identify which sides of the right triangle are given. The equation a² + b² = c² represents the Pythagorean theorem, where a and b are the lengths of the two legs of the right triangle, and c is the length of the hypotenuse.
Let's assume that a and b are the given side lengths, and we need to find the length of the hypotenuse (c).
Using the Pythagorean theorem, we have:
a² + b² = c²
Substituting the given values, we have:
a² + 6² = 13²
Simplifying:
a² + 36 = 169
Next, we isolate the variable a by subtracting 36 from both sides:
a² = 169 - 36
a² = 133
To find the value of a, we can take the square root of both sides:
√(a²) = √(133)
a = √(133)
So the length of the missing side is √(133), which is approximately 11.54 (rounded to two decimal places).