1. **Problem Statement:** We need to find the length of segment $JN$ in the given right triangle configuration. 2. **Given:** - Triangle $KLJ$ is right-angled at $L$. - Segment $KM$ is horizontal, intersecting vertical segment $JL$ at $M$, forming right triangle $KMJ$ with right angle at $M$. - $KN = 6.9$ units. - $JM = 4.4$ units. - $ML = 3.6$ units. 3. **Goal:** Find $JN$ rounded to the nearest tenth. 4. **Step 1: Understand the triangle setup.** - Since $JL$ is vertical and $KM$ is horizontal, $M$ lies on $JL$. - $JM + ML = JL = 4.4 + 3.6 = 8.0$ units. 5. **Step 2: Use the right triangle $KLJ$.** - Right angle at $L$ means $KL$ and $JL$ are perpendicular. - We know $JL = 8.0$ units. 6. **Step 3: Use the right triangle $KMJ$.** - Right angle at $M$ means $KM$ is horizontal and $JM$ is vertical. - $JM = 4.4$ units (vertical leg). - $KN = 6.9$ units is the hypotenuse of triangle $KMN$ (since $N$ lies on $JK$). 7. **Step 4: Find $JN$.** - $JN$ is the horizontal leg of right triangle $KMJ$. - Use Pythagorean theorem in triangle $KMJ$: $$KN^2 = JN^2 + JM^2$$ $$6.9^2 = JN^2 + 4.4^2$$ 8. **Step 5: Calculate $JN$:** $$JN^2 = 6.9^2 - 4.4^2 = 47.61 - 19.36 = 28.25$$ $$JN = \sqrt{28.25} \approx 5.3$$ **Final answer:** $$JN \approx 5.3$$ units (rounded to the nearest tenth).