1. **Problem statement:** Find the length of segment $LK$ given the other segment lengths in the geometric figure. 2. **Given data:** - $KN = 9.76$ - $LN = 18.79$ 3. **Approach:** Since $L$, $K$, and $N$ form a right triangle (implied by right-angle markers), we can use the Pythagorean theorem: $$LK^2 + KN^2 = LN^2$$ 4. **Apply the formula:** $$LK^2 = LN^2 - KN^2$$ Substitute the values: $$LK^2 = 18.79^2 - 9.76^2$$ Calculate squares: $$LK^2 = 353.1841 - 95.2576$$ $$LK^2 = 257.9265$$ 5. **Find $LK$ by taking the square root:** $$LK = \sqrt{257.9265}$$ $$LK \approx 16.06$$ 6. **Answer:** The length of segment $LK$ is approximately $16.06$ units.