1. **State the problem:** We have a right triangle HIJ with a right angle at vertex I. Angle H is 27°. Side IJ (adjacent to angle H) is 6. Side JI (opposite angle H) is labeled $x$. 2. **Identify the trigonometric function:** Since we know the adjacent side (IJ = 6) and want to find the opposite side ($x$) relative to angle H, we use the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Write the equation:** $$\tan(27^\circ) = \frac{x}{6}$$ 4. **Solve for $x$:** Multiply both sides by 6: $$6 \times \tan(27^\circ) = x$$ 5. **Calculate the value:** $$x = 6 \times \tan(27^\circ)$$ Using a calculator: $$\tan(27^\circ) \approx 0.5095$$ So, $$x \approx 6 \times 0.5095 = 3.057$$ 6. **Round to the nearest tenth:** $$x \approx 3.1$$ **Final answer:** $$x = 3.1$$