Question

Find height of triangle in a 45-45-90 triangle knowing one side

Answer 1

Look at the picture.
It's the isosceles triangle.
Use the Pythagorean theorem:

`x^2=a^2+a^2\\\\x^2=2a^2\\\\x=√(2a^2)\\\\x=a\sqrt2`
Therefore:
If you are knowing the length of side a, then
`x=a\sqrt2`.
If you are knowing the length of side x, then
`a=(x\sqrt2)/(2)`