1. **State the problem:** We have a right triangle GHI with a right angle at H. Side GH is 5.6 units, angle at I is 29°, and GI is the hypotenuse labeled $x$. We need to find $x$. 2. **Identify the sides relative to angle I:** - GH is opposite angle I. - HI is adjacent to angle I. - GI is the hypotenuse. 3. **Use the sine function:** Since sine relates the opposite side to the hypotenuse, we use: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ Here, $\theta = 29^\circ$, opposite side = 5.6, hypotenuse = $x$. 4. **Set up the equation:** $$\sin(29^\circ) = \frac{5.6}{x}$$ 5. **Solve for $x$:** $$x = \frac{5.6}{\sin(29^\circ)}$$ 6. **Calculate $\sin(29^\circ)$:** $$\sin(29^\circ) \approx 0.4848$$ 7. **Find $x$:** $$x = \frac{5.6}{0.4848} \approx 11.55$$ 8. **Round to the nearest tenth:** $$x \approx 11.6$$ **Final answer:** $x = 11.6$