Question 1117085
 In triangle, ABC, angle ABC=90, and point D lie on segment BC such that AD is an angle bisector.
 If AB=105 and BD=42, then find AC.
:
Draw out the triangle as described.
A smaller right triangle ABD is also formed.
 A portion of the bisected angle (BAC) forms an angle (x) of this triangle.
Find this angle (x)  using the tangent
tan(x) = {{{42/105}}}
x = 21.8 degrees
the Angle BAC = 2 * 21.8 = 43.6 degrees
AC is the hypotenuse, find AC using the cosine of 43.6 degree
cos(43.8) = {{{105/h}}}
h = {{{105/cos(43.6)}}}
h = 145 = AC