1. **Problem Statement:** We are given a right triangle with vertices B, C, and A. Side BC is vertical with length 2 units, side BA is the hypotenuse with length 5 units, and angle C is a right angle (90°). We need to find the measure of angle B, rounded to the nearest hundredth. 2. **Relevant Formula:** In a right triangle, the sine, cosine, or tangent of an angle can be used to find the angle measure. Here, we can use the sine function: $$\sin(\angle B) = \frac{\text{opposite side}}{\text{hypotenuse}}$$ 3. **Identify sides relative to angle B:** - Opposite side to angle B is side AC. - Adjacent side to angle B is side BC (length 2). - Hypotenuse is side BA (length 5). 4. **Find length of side AC using the Pythagorean theorem:** $$AC = \sqrt{BA^2 - BC^2} = \sqrt{5^2 - 2^2} = \sqrt{25 - 4} = \sqrt{21}$$ 5. **Calculate sine of angle B:** $$\sin(\angle B) = \frac{AC}{BA} = \frac{\sqrt{21}}{5}$$ 6. **Calculate angle B:** $$\angle B = \arcsin\left(\frac{\sqrt{21}}{5}\right)$$ Using a calculator: $$\angle B \approx \arcsin(0.9165) \approx 66.42^\circ$$ **Final answer:** $$\boxed{66.42^\circ}$$