In the image, you're asked to find the distance $AB$ in a right-angled triangle, where:

• $AD = 4 \, \text{cm}$
• $BC = 3 \, \text{cm}$

From the diagram, we can infer that the triangle $ABC$ forms a right triangle, and we can use the Pythagorean theorem to calculate the length of $AB$. The Pythagorean theorem states:

$AB^2 = AD^2 + BC^2$

Substituting the given values:

$AB^2 = 4^2 + 3^2 = 16 + 9 = 25$

Thus, $AB = \sqrt{25} = 5 \, \text{cm}$.

Answer:

The distance $AB$ is $5 \, \text{cm}$.

Would you like further details or have any questions?

Here are five related questions to deepen your understanding:

1. How is the Pythagorean theorem applied in different types of triangles?
2. Can the Pythagorean theorem be used to find any other side of a right triangle?
3. What happens if one of the triangle's side lengths is missing or unknown?
4. How do we know that triangle $ABC$ is a right triangle from the diagram?
5. What is the relationship between the sides of a triangle and the angles inside it?

Tip: Always check if a triangle is right-angled before applying the Pythagorean theorem.