1. The problem asks to find the acute angles in a right triangle with vertices A, B, and C, where B is the right angle. 2. Given: side opposite B (hypotenuse) = 7, side opposite C = 6, and angle B = 90°. 3. To find the acute angle at C, use the sine function: $$\sin(C) = \frac{\text{opposite side to } C}{\text{hypotenuse}} = \frac{6}{7}$$. 4. Calculate angle C: $$C = \arcsin\left(\frac{6}{7}\right)$$. 5. Using a calculator, $$C \approx 59.04^\circ$$. 6. Since the triangle's angles sum to 180° and B is 90°, angle A is: $$A = 90^\circ - C = 90^\circ - 59.04^\circ = 30.96^\circ$$. 7. Both angles A and C are acute angles. 8. Final answer: acute angles are approximately $$30.96^\circ$$ at A and $$59.04^\circ$$ at C.