Question 340929
the hypotenuse of a right triangle is twice as long as the height. determine the height as a function of the base b.
.
Because it is a "right triangle" we can apply Pythagorean theorem:
Let h = height of triangle
then
2h = hypotenuse
.
{{{ (2h)^2 = h^2 + b^2 }}}
{{{ 4h^2 = h^2 + b^2 }}}
{{{ 3h^2 = b^2 }}}
{{{ h^2 = b^2/3 }}}
{{{ h = sqrt(b^2/3) }}}
{{{ h = b*sqrt(1/3) }}}
{{{ h = b*sqrt(3)/3 }}}