[Manish]

Answer is approximately 552.5 cm^2

[Manish]

To find the height of a right-angled triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the base of the triangle is 6 cm, and the side opposite the right angle is 10 cm. Let’s denote the height as ‘h’.

According to the Pythagorean theorem:

(base)^2 + (height)^2 = (hypotenuse)^2

Substituting the known values:

6^2 + h^2 = 10^2

36 + h^2 = 100

h^2 = 100 – 36

h^2 = 64

Taking the square root of both sides:

h = √64

h = 8 cm

Therefore, the height of the right-angled triangle is 8 cm.