1. **State the problem:** We have a right triangle ABC with angle B as the right angle, angle A = 11°, side AB (adjacent to angle A) = 27, and hypotenuse AC = x. We need to find $x$ rounded to the nearest hundredth. 2. **Formula used:** In a right triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 11^\circ$, adjacent side = 27, hypotenuse = $x$. $$\cos(11^\circ) = \frac{27}{x}$$ 4. **Solve for $x$:** Multiply both sides by $x$ and then divide both sides by $\cos(11^\circ)$: $$x \cdot \cos(11^\circ) = 27$$ $$\cancel{x} \cdot \cos(11^\circ) = 27 \implies x = \frac{27}{\cos(11^\circ)}$$ 5. **Calculate the value:** $$x = \frac{27}{\cos(11^\circ)} \approx \frac{27}{0.9816} \approx 27.51$$ 6. **Final answer:** Rounded to the nearest hundredth, $x = 27.51$. Note: The answer 141.48 given in the prompt seems incorrect based on the triangle configuration and trigonometric calculation.