Question: \angle A = \degree Round your answer to the nearest hundredth. A 5 ? B 3 C bottom-right: right triangle with vertices B at bottom-left, C at bottom-right, and A at top; BC = 3, BA = 5, and angle at C is marked as a right angle.\angle A = [ ]\degree Round your answer to the nearest hundredth. A ? 5 B 3 C Right triangle ABC with right angle at C; BC = 3, BA = 5, and the unknown angle is at A. position_hint=bottom-right

1. **Problem Statement:** We have a right triangle ABC with a right angle at C. The side lengths are given as $BC = 3$ and $BA = 5$. We need to find the measure of angle $\angle A$ rounded to the nearest hundredth of a degree. 2. **Identify the sides relative to angle $A$:** - Hypotenuse: $BA = 5$ - Opposite side to angle $A$: $BC = 3$ - Adjacent side to angle $A$: $AC$ (unknown) 3. **Formula to use:** Since we know the hypotenuse and the side opposite to angle $A$, we use the sine function: $$\sin(\angle A) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{BC}{BA} = \frac{3}{5}$$ 4. **Calculate $\sin(\angle A)$:** $$\sin(\angle A) = \frac{3}{5} = 0.6$$ 5. **Find $\angle A$ using inverse sine:** $$\angle A = \sin^{-1}(0.6)$$ 6. **Calculate the angle:** Using a calculator, $$\angle A \approx 36.86989765^\circ$$ 7. **Round to the nearest hundredth:** $$\angle A \approx 36.87^\circ$$ **Final answer:** $$\boxed{36.87^\circ}$$