1. **State the problem:** We have a TV with a diagonal length of 54 inches and a width of 40 inches. We need to find the height of the TV. 2. **Formula used:** For a rectangle, the diagonal $d$, width $w$, and height $h$ satisfy the Pythagorean theorem: $$d^2 = w^2 + h^2$$ 3. **Apply the formula:** Substitute $d=54$ and $w=40$: $$54^2 = 40^2 + h^2$$ 4. **Calculate squares:** $$2916 = 1600 + h^2$$ 5. **Isolate $h^2$:** $$h^2 = 2916 - 1600$$ $$h^2 = 1316$$ 6. **Find $h$ by taking the square root:** $$h = \sqrt{1316}$$ 7. **Calculate the square root and round to the nearest tenth:** $$h \approx 36.3$$ **Final answer:** The height of the TV is approximately **36.3 inches**.