To solve for $AB$, we use the Pythagorean theorem, as $\triangle ABC$ is a right triangle with $\angle BAC = 90^\circ$.

Steps:

1. Pythagorean Theorem: $BC^2 = AB^2 + AC^2$ Substituting the known values: $(4.25)^2 = AB^2 + (3.75)^2$

2. Square the lengths: $4.25^2 = 18.0625, \quad 3.75^2 = 14.0625$

3. Simplify the equation: $18.0625 = AB^2 + 14.0625$ $AB^2 = 18.0625 - 14.0625 = 4$

4. Solve for $AB$: $AB = \sqrt{4} = 2 \, \text{cm}$

Final Answer:

$AB = 2 \, \text{cm}$

Would you like a step-by-step diagram or further clarification?

Related Questions:

1. What is the length of the hypotenuse of a triangle with different dimensions?
2. Can the Pythagorean theorem be used for non-right triangles?
3. How would you calculate $AB$ if the angle $\angle BAC$ were not $90^\circ$?
4. What is the significance of a right triangle in geometry?
5. How would errors in measurements affect the calculation?

Tip:

Always verify if the triangle is right-angled before applying the Pythagorean theorem!