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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.

The hypotenuse and the base of a right angled triangle is 10 cm and 6 cm respectively. What is the height of the triangle?

Learn how to determine the height of a right-angled triangle with a hypotenuse of 10 cm and a base of 6 cm using the Pythagorean theorem. This step-by-step solution covers key geometric concepts and is ideal for students in Grades 7-9.

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