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, 42AC=42 and D, C, equals, 11, commaDC=11, 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 satisfies (leg)^2 = (hypotenuse)·(adjacent hypotenuse segment). Thus

BC^2 = AC·DC = 42·11 = 462,

so BC = sqrt(462).