document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #732053 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
In triangle, ABC, angle ABC=90, and point D lie on segment BC such that AD is an angle bisector.
\n" ); document.write( " If AB=105 and BD=42, then find AC.
\n" ); document.write( ":
\n" ); document.write( "Draw out the triangle as described.
\n" ); document.write( "A smaller right triangle ABD is also formed.
\n" ); document.write( " A portion of the bisected angle (BAC) forms an angle (x) of this triangle.
\n" ); document.write( "Find this angle (x) using the tangent
\n" ); document.write( "tan(x) = \"42%2F105\"
\n" ); document.write( "x = 21.8 degrees
\n" ); document.write( "the Angle BAC = 2 * 21.8 = 43.6 degrees
\n" ); document.write( "AC is the hypotenuse, find AC using the cosine of 43.6 degree
\n" ); document.write( "cos(43.8) = \"105%2Fh\"
\n" ); document.write( "h = \"105%2Fcos%2843.6%29\"
\n" ); document.write( "h = 145 = AC
\n" ); document.write( " \n" ); document.write( "
\n" );