1. **State the problem:** We have a right triangle with one leg $a=20$ and hypotenuse $c=29$. We need to find the other leg $b$ and the trigonometric ratios $\sin(B)$, $\cos(A)$, and $\tan(A)$. 2. **Formula used:** In a right triangle, by the Pythagorean theorem, the legs and hypotenuse satisfy $$a^2 + b^2 = c^2.$$ 3. **Find the other leg $b$:** Substitute the known values: $$20^2 + b^2 = 29^2$$ $$400 + b^2 = 841$$ $$b^2 = 841 - 400 = 441$$ $$b = \sqrt{441} = 21.$$ 4. **Find the trigonometric ratios:** - Angle $A$ is opposite leg $a=20$, adjacent leg $b=21$, hypotenuse $c=29$. - Angle $B$ is opposite leg $b=21$, adjacent leg $a=20$, hypotenuse $c=29$. 5. Calculate each ratio: - $\sin(B) = \frac{\text{opposite to } B}{\text{hypotenuse}} = \frac{b}{c} = \frac{21}{29}.$ - $\cos(A) = \frac{\text{adjacent to } A}{\text{hypotenuse}} = \frac{b}{c} = \frac{21}{29}.$ - $\tan(A) = \frac{\text{opposite to } A}{\text{adjacent to } A} = \frac{a}{b} = \frac{20}{21}.$ **Final answers:** $$b = 21,$$ $$\sin(B) = \frac{21}{29},$$ $$\cos(A) = \frac{21}{29},$$ $$\tan(A) = \frac{20}{21}.$$