Proof:

To prove that angle B is equal to angle Q, we will use the given information that sin(B) = sin(Q) and the fact that both B and Q are acute angles.

1. Understanding acute angles:
An acute angle is an angle that measures less than 90 degrees. In other words, an acute angle is smaller than a right angle.

2. Definition of sine:
The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

3. Using the definition of sine:
Since the given angles B and Q are acute, we can construct right triangles where angle B and angle Q are included. Let's consider a right triangle ABC for angle B and a right triangle PQR for angle Q.

In triangle ABC, angle B is acute. Let BC be the side opposite angle B and AC be the hypotenuse.

In triangle PQR, angle Q is acute. Let QR be the side opposite angle Q and PR be the hypotenuse.

According to the definition of sine, sin(B) = BC/AC and sin(Q) = QR/PR.

4. Equating the sine values:
Given that sin(B) = sin(Q), we can equate the two expressions:

BC/AC = QR/PR

5. Understanding the equality:
Since BC/AC = QR/PR, we can conclude that the ratios of the side opposite the angle to the hypotenuse are equal in both triangles.

This means that the ratios of the lengths of the sides opposite angle B and angle Q to their respective hypotenuses are equal.

6. Applying the concept of similar triangles:
By the concept of similar triangles, if the ratios of corresponding sides of two triangles are equal, then the triangles are similar.

In this case, triangle ABC and triangle PQR are similar triangles.

7. Corresponding angles of similar triangles:
In similar triangles, corresponding angles are equal.

Therefore, angle B in triangle ABC is equal to angle Q in triangle PQR.

8. Conclusion:
We have shown that angle B is equal to angle Q using the given information that sin(B) = sin(Q) and the fact that both B and Q are acute angles.