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A triangle has corners at points A, B, and C. Side AB has a length of #9 #. The distance between the intersection of point A's angle bisector with side BC and point B is #6 #. If side AC has a length of #16 #, what is the length of side BC?

Answer 1

Wyatt Anderson

#BC=16 2/3" units"#

Let D be the point on BC where the angle bisector intersects BC.

#rArrBC=BD+DC#

We are given BD = 6 and require to find DC

#"Using the "color(blue)" Angle bisector theorem"#

#color(red)(bar(ul(|color(white)(2/2)color(black)((AB)/(AC)=(BD)/(DC))color(white)(2/2)|)))#

Substitute given values into this equation.

#9/16=6/(DC)#

#color(blue)"cross-multiply"#

#9xxDC=6xx16#

#rArrDC=(6xx16)/9=32/3#

#rArrBC=6+32/3=16 2/3" units"#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.