Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse ACAC. If BC=12BC=12 and DC=3,DC=3, what is the length of \overline{AC}?AC? (Note: the figure is not drawn to scale.)
Triangle BCD is right with hypotenuse BC =12 and leg CD = 3
So BD^2 = BC^2 - CD^2 = 12^2 - 3^2 = 144 - 9 = 135
And.....like the problem you submitted before
CD / BD = BD / DA cross-multiply
CD * DA = BD^2
3 * DA = 135
DA = 135 / 3 = 45
So CA = CD + DA = 3 + 45 = 48
