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A triangle has corners at points A, B, and C. Side AB has a length of #36 #. The distance between the intersection of point A's angle bisector with side BC and point B is #15 #. If side AC has a length of #27 #, what is the length of side BC?

Answer 1

26.25

Here is a sketch (not to scale)

To calculate the length of BC , we require the length of DC.

Using the#color(blue)"Angle bisector theorem"#
For the triangle ABC given, this is.

#color(red)(|bar(ul(color(white)(a/a)color(black)((BD)/(DC)=(AB)/(AC))color(white)(a/a)|)))#
Substitute the appropriate values into the ratio.

#rArr15/(DC)=36/27#
now cross-multiply

#rArrDCxx36=15xx27rArrDC=(15xx27)/36#
Thus DC #=45/4=11 1/4=11.25#
length of BC = BD + DC = 15 + 11.25 = 26.25

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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.