1. **Problem Statement:** Given a right triangle ABC with right angle at A, side AB = 4, side AC = 3, and BC is the hypotenuse. Find the measure of the shaded angle (assumed to be angle B or C). 2. **Formula Used:** To find an angle in a right triangle, use the trigonometric ratios: sine, cosine, or tangent. 3. **Step 1: Calculate the hypotenuse BC** Using the Pythagorean theorem: $$BC = \sqrt{AB^2 + AC^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$$ 4. **Step 2: Find angle B** Angle B is opposite side AC (3) and adjacent to AB (4). Use tangent: $$\tan(B) = \frac{\text{opposite}}{\text{adjacent}} = \frac{3}{4}$$ 5. **Step 3: Calculate angle B** $$B = \tan^{-1}\left(\frac{3}{4}\right) \approx 36.87^\circ$$ 6. **Step 4: Find angle C** Since the triangle is right angled at A, angles B and C sum to 90 degrees: $$C = 90^\circ - B = 90^\circ - 36.87^\circ = 53.13^\circ$$ **Final answer:** The shaded angle (if angle B) is approximately $36.87^\circ$. If the shaded angle is angle C, it is approximately $53.13^\circ$.