To find the length of the missing side of a right triangle when you know the hypotenuse and one leg, you can use the Pythagorean theorem:

$a^2 + b^2 = c^2$

Where:

• $a$ and $b$ are the legs of the triangle,
• $c$ is the hypotenuse.

In your case:

• Hypotenuse $c = 8 \, \text{cm}$,
• One leg $b = 5 \, \text{cm}$,
• We need to find the length of the other leg $a$.

Using the Pythagorean theorem:

$a^2 + 5^2 = 8^2$ $a^2 + 25 = 64$ $a^2 = 64 - 25$ $a^2 = 39$ $a = \sqrt{39} \approx 6.24 \, \text{cm}$

So, the length of the other side is approximately 6.24 cm.

Let me know if you'd like further details or have any questions! Here's some related information:

1. How do you calculate the area of a right triangle?
2. What happens if the hypotenuse is not the longest side?
3. What are the trigonometric ratios for a right triangle?
4. How can you verify a triangle is a right triangle using the Pythagorean theorem?
5. Can the Pythagorean theorem be used for non-right triangles?

Tip: The Pythagorean theorem only works for right triangles.