How do I calculate the height of a right angle triangle when given the base and longer side?

Question

A right angle triangle with diagonal side length 10 units and base of 6 units is how high on its third side?

Answer 1

A right angle triangle with diagonal side length 10 units and base of 6 units is how high on its third side?

Pythagorean theorem:

base^2 + height^2 = hypotenuse^2 (the diagonal part)

6^2 + height^2 = 10^2

36 + height^2 = 100

height^2 = 64

height = 8

Answer 2

If you have a right angled triangle and you know the hypotenuse and one cathetus, first you need to find the other cathetus. You can find it with the formula : a² + b² = c² where a is one cathetus and c is the hypotenuse. To find the other cathetus that here its b you need to use the formula : b² = c² - a². You know the value of a and c so you can solve it quickly. You also can use the other formula which practicaly is the same : b = √ c² - a². Now you know the other cathetus. In a right angled triangle cathetus is height as well with the other cathetus like a base. Thats all.