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, D, equals, 11AD=11 and A, C, equals, 30, commaAC=30, what is the length of start overline, A, B, end overline
AB
in simplest radical form?

Answer 1

In a right triangle with altitude from the right angle to the hypotenuse, the leg satisfies AB^2 = AD · AC. So

AB^2 = 11 · 30 = 330,

hence AB = √330.