To find the unknown side of the right triangle, we can apply the Pythagorean theorem, which states:

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

where:

• $a$ and $b$ are the legs of the right triangle, and
• $c$ is the hypotenuse (the side opposite the right angle).

In your case, the vertical leg is 7 cm and the horizontal leg is 8 cm. We need to find the hypotenuse $c$.

Step 1: Apply the Pythagorean theorem

$7^2 + 8^2 = c^2$ $49 + 64 = c^2$ $113 = c^2$

Step 2: Solve for $c$

Take the square root of both sides: $c = \sqrt{113} \approx 10.6 \text{ cm}$

So, the length of the hypotenuse is approximately 10.6 cm.

Would you like any more details or have further questions about this problem?

Here are 5 related questions for you:

1. How would the Pythagorean theorem change if the triangle were an isosceles right triangle?
2. How do you find the area of a right triangle using its legs?
3. Can the Pythagorean theorem be used to find one of the legs if the hypotenuse and one leg are known?
4. What happens if the triangle is not a right triangle? How do you find the sides?
5. How does the Pythagorean theorem relate to trigonometric ratios in right triangles?

Tip: To practice, you can try using the Pythagorean theorem on triangles with different leg lengths to get familiar with solving for the unknown side!