Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse ACAC. If AB=8AB=8 and AD=4,AD=4, what is the length of \overline{AC}?AC? (Note: the figure is not drawn to scale.)
As before....triangle ABD is right
AB^2 - AD^2 = BD^2
8^2 - 4^2 =
64 - 16 =
48 = BD^2
So
AD / BD = BD / DC
4 / BD = BD / DC cross-multiply
4 DC = BD^2
4DC = 48
DC = 48 / 4 = 12
AC = AD + DC = 4 + 12 = 16
