1. **State the problem:** We have a right triangle with legs 33 and 44, and hypotenuse 55. We want to find the angle $\theta$ at the top-left vertex. 2. **Formula used:** To find an angle in a right triangle, we use the trigonometric ratios. Here, we can use the sine, cosine, or tangent functions. For example, $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Identify sides relative to $\theta$:** The side opposite $\theta$ is 33, the hypotenuse is 55, and the adjacent side is 44. 4. **Calculate $\sin(\theta)$:** $$\sin(\theta) = \frac{33}{55}$$ 5. **Simplify the fraction:** $$\sin(\theta) = \frac{\cancel{11} \times 3}{\cancel{11} \times 5} = \frac{3}{5}$$ 6. **Find $\theta$ using inverse sine:** $$\theta = \sin^{-1}\left(\frac{3}{5}\right)$$ 7. **Calculate the angle:** $$\theta \approx 36.87^\circ$$ **Final answer:** $$\boxed{\theta \approx 36.87^\circ}$$