1. **Problem:** Calculate the value of $\theta$ to the nearest hundredth using trigonometric ratios and inverse trig functions for the first triangle with angle 45°, leg $x$, and hypotenuse 11.31. 2. **Formula:** Use the sine function since we have the opposite side $x$ and hypotenuse 11.31: $$\sin(45^\circ) = \frac{x}{11.31}$$ 3. **Calculate $x$:** $$x = 11.31 \times \sin(45^\circ)$$ Using a calculator: $$\sin(45^\circ) = 0.7071$$ So, $$x = 11.31 \times 0.7071 = 7.999$$ 4. **Answer:** The length of leg $x$ is approximately 8.00. --- Since the user asked for the first problem only, we stop here.