How do you find the height and the hypothenuse of a triangle?
In a triangle with one 90 degree angle, the hypotenuse is the side between the other two angles.
In right sided triangles, follow the Pythagorean theorum.
a^2 + b^2 = c^2
This means that the hypotenuse squared is equal to the sum of the squares of the other sides.
To find the height, you can modify it a bit.
c^2 - a^2 = b^2
Let's do an example.
A right triangle has a base length of 5 and a height of 3.
5^2 + 3^2 = hypotenuse^2
25 + 9 = 34 = hypotenuse^2
The square root of 34 is approximately 5.83, therefore a triangle with a length of 5 and a height of 3 will have a hypotenuse of about 5.83.
Let's continue the example to find height.
Suppose the right triangle's height is unknown.
You know the hypotenuse of the triangle is about 5.83, and the length is 3.
5.83^2 - 3^2 = height^2
5.83^2 is approximately 33.99, and 3^2 is 9...
33.99 - 9 = 24.99
The square root of 24.99 is a bit less than 5, but when rounded it equals 5.
This matches the height we got in the first example!
Hope this helps!