Question

Given right triangle A, B, CABC with altitude start overline, B, D, end overline
BD
drawn to hypotenuse start overline, A, C, end overline
AC
. If A, C, equals, 13AC=13 and D, C, equals, 3, commaDC=3, what is the length of start overline, B, C, end overline
BC
in simplest radical form?

Answer 1

In a right triangle with altitude from the right angle to the hypotenuse, each leg squared equals the hypotenuse times the adjacent hypotenuse segment. So

BC^2 = AC · DC = 13 · 3 = 39,

hence BC = sqrt(39).