1. **State the problem:** We have a right triangle with vertices A, B, and a third vertex. The side opposite angle $\alpha$ at vertex B is $d=24$, the hypotenuse (side opposite the right angle at A) is $y=26$, and we need to find the angle $\alpha$. 2. **Formula used:** In a right triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the hypotenuse: $$\sin(\alpha) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, the opposite side to $\alpha$ is $d=24$ and the hypotenuse is $y=26$. $$\sin(\alpha) = \frac{24}{26}$$ 4. **Simplify the fraction:** $$\sin(\alpha) = \frac{\cancel{24}}{\cancel{26}} = \frac{12}{13}$$ 5. **Calculate the angle $\alpha$:** Use the inverse sine function (arcsin) to find $\alpha$: $$\alpha = \sin^{-1}\left(\frac{12}{13}\right)$$ 6. **Evaluate the angle:** $$\alpha \approx \sin^{-1}(0.9231) \approx 67.38^\circ$$ 7. **Final answer:** The angle $\alpha$ is approximately **67.38 degrees** rounded to two decimal places.