This image depicts a right-angled triangle $\triangle ABC$ with:

• $AC = 12 \, \text{m}$ (the base),
• $BC = 5 \, \text{m}$ (the height),
• $AB = c$ (the hypotenuse).

To solve for $c$, the hypotenuse, we can use the Pythagorean theorem:

$c^2 = AC^2 + BC^2$

Substituting the known values:

$c^2 = 12^2 + 5^2$ $c^2 = 144 + 25 = 169$ $c = \sqrt{169} = 13 \, \text{m}$

Thus, the hypotenuse $c$ is 13 meters.

Do you want more details or have any questions? Here are 5 related questions:

1. How do you calculate the area of the triangle?
2. What is the perimeter of the triangle after finding the hypotenuse?
3. How can you find the angles of the triangle using trigonometry?
4. Can the Pythagorean theorem be used in non-right triangles?
5. How would the calculation change if one of the sides were unknown instead?

Tip: In any right triangle, the hypotenuse is always the longest side.