Given:
- Angle B and angle Q are acute angles.
- sin B = sin Q

To prove:
- Angle B = Angle Q

Proof:

Step 1: Understanding the problem
To solve this problem, we need to prove that if sin B is equal to sin Q, then angle B is equal to angle Q. In other words, we need to show that the equality of the sines of two acute angles implies the equality of the angles themselves.

Step 2: Understanding the concept of sine function
The sine function (sin) relates the ratio of the length of the side opposite to an angle in a right triangle to the length of the hypotenuse. In other words, sin B = opposite side / hypotenuse and sin Q = opposite side / hypotenuse.

Step 3: Equating the sines of angles
Given that sin B = sin Q, we can equate the ratios:
opposite side of angle B / hypotenuse = opposite side of angle Q / hypotenuse

Step 4: Simplifying the equation
Since the hypotenuse is the same for both angles B and Q, we can cancel it out from the equation:
opposite side of angle B = opposite side of angle Q

Step 5: Understanding the concept of opposite sides
In a right triangle, the side opposite to an acute angle is unique to that angle. Therefore, if the opposite sides of two angles are equal, the angles themselves must be equal.

Step 6: Concluding the proof
Since the opposite sides of angles B and Q are equal (as given by the equation opposite side of angle B = opposite side of angle Q), we can conclude that angle B is equal to angle Q.

Therefore, the proof is complete.