Question

The hypotenuse of a right triangle is twice as long as the height. Determine the height as a function of the base b.

Answer 1

Given that we know Pythagorean theorem \[a^2 + b^2 = c^2\] and \[c = 2a\]
We can substitute the second equation into the first equation giving us \[a^2 + b^2 = (2a)^2\]
Which results in \[a^2 + b^2 = 4a^2\] And then solve for b.

Answer 2

You have a 1,2,sqrt(3) triangle scaled by h.

So the height is base * 1/sqrt3. = h