1. **State the problem:** We have a right triangle with one leg of length 23, an angle of 47°, and we need to find the other leg $a$, the hypotenuse $c$, and the remaining angle $B$. 2. **Identify known values:** - One leg: $23$ - Angle: $47^\circ$ - Right angle: $90^\circ$ 3. **Find angle $B$:** Since the sum of angles in a triangle is $180^\circ$ and one angle is $90^\circ$, the other non-right angle is $$B = 90^\circ - 47^\circ = 43^\circ$$ 4. **Use trigonometric ratios:** Let the side opposite $47^\circ$ be $a$, the side adjacent to $47^\circ$ be $23$, and hypotenuse $c$. - Using tangent to find $a$: $$\tan(47^\circ) = \frac{a}{23}$$ Multiply both sides by 23: $$a = 23 \times \tan(47^\circ)$$ Calculate: $$a \approx 23 \times 1.0724 = 24.7$$ 5. **Find hypotenuse $c$ using cosine:** $$\cos(47^\circ) = \frac{23}{c}$$ Multiply both sides by $c$: $$c \cos(47^\circ) = 23$$ Divide both sides by $\cos(47^\circ)$: $$\cancel{c} = \frac{23}{\cos(47^\circ)}$$ Calculate: $$c \approx \frac{23}{0.681998} = 33.7$$ **Final answers:** - $B = 43^\circ$ - $a = 24.7$ - $c = 33.7$