1. **Problem Statement:** We have a right triangle with side lengths 7, 24, and 25. We need to find $\sin B$, $\tan B$, and $\cos B$ where angle $B$ is at the bottom-right vertex. 2. **Identify sides relative to angle B:** - Hypotenuse ($AB$) = 25 (longest side opposite the right angle) - Opposite side to angle $B$ = $AC = 24$ - Adjacent side to angle $B$ = $CB = 7$ 3. **Recall trigonometric definitions:** $$\sin B = \frac{\text{opposite}}{\text{hypotenuse}}$$ $$\cos B = \frac{\text{adjacent}}{\text{hypotenuse}}$$ $$\tan B = \frac{\text{opposite}}{\text{adjacent}}$$ 4. **Calculate each ratio:** $$\sin B = \frac{24}{25}$$ $$\tan B = \frac{24}{7}$$ $$\cos B = \frac{7}{25}$$ 5. **Simplify if possible:** These fractions are already in simplest form. **Final answers:** $$\sin B = \frac{24}{25}$$ $$\tan B = \frac{24}{7}$$ $$\cos B = \frac{7}{25}$$