1. **State the problem:** We have a right triangle NSB with a right angle at N. Segment NW is perpendicular to the hypotenuse BS, creating two smaller right triangles. We know NB = 12 units and WS = 16.1 units, and we need to find BW. 2. **Identify the triangles:** Since NW is perpendicular to hypotenuse BS, triangles NWB and NWS are similar to triangle NSB by the AA similarity criterion (right angle and shared angle). 3. **Use similarity ratios:** The segments on the hypotenuse satisfy the relation $BW \times WS = NB^2$ because the altitude to the hypotenuse in a right triangle creates two segments whose product equals the square of the leg adjacent to the altitude. 4. **Apply the formula:** $$BW \times 16.1 = 12^2$$ $$BW \times 16.1 = 144$$ 5. **Solve for BW:** $$BW = \frac{144}{16.1} \approx 8.944$$ 6. **Round to the nearest tenth:** $$BW \approx 8.9$$ **Final answer:** $BW = 8.9$ units.