To determine the height of the right-angled triangle given the hypotenuse (10 cm) and the base (6 cm), we can use the Pythagorean theorem:

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

where:

• $c$ is the hypotenuse,
• $a$ is the base,
• $b$ is the height (which we need to find).

Rearranging the formula to solve for $b$:

$b = \sqrt{c^2 - a^2}$

Substitute $c = 10$ cm and $a = 6$ cm:

$b = \sqrt{10^2 - 6^2}$ $b = \sqrt{100 - 36}$ $b = \sqrt{64}$ $b = 8 \, \text{cm}$

So, the height of the triangle is 8 cm.

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

Here are some related questions to deepen understanding:

1. What is the Pythagorean theorem, and why is it useful in right-angled triangles?
2. How can we determine if a triangle is a right triangle using side lengths?
3. Can the Pythagorean theorem be used in non-right triangles?
4. What is the significance of the hypotenuse in a right triangle?
5. How would the calculation change if the base and height were swapped?

Tip: In a right triangle, the Pythagorean theorem only applies between the hypotenuse and the other two sides, which are perpendicular to each other.