1. **Problem Statement:** We have a right triangle inscribed in a circle. The triangle has sides labeled 10.4, 8.4, and $x$, with a right angle between the sides 8.4 and $x$. We need to find the length of $x$. 2. **Formula Used:** Since the triangle has a right angle, we can use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are the legs of the right triangle, and $c$ is the hypotenuse. 3. **Identify the sides:** - The side opposite the right angle (hypotenuse) is 10.4. - The two legs are 8.4 and $x$. 4. **Apply the Pythagorean theorem:** $$8.4^2 + x^2 = 10.4^2$$ 5. **Calculate squares:** $$8.4^2 = 70.56$$ $$10.4^2 = 108.16$$ 6. **Substitute and solve for $x^2$:** $$70.56 + x^2 = 108.16$$ $$x^2 = 108.16 - 70.56 = 37.6$$ 7. **Find $x$ by taking the square root:** $$x = \sqrt{37.6} \approx 6.13$$ **Final answer:** $$x \approx 6.13$$ This means the length of the segment $x$ is approximately 6.13 units.