# A triangle has corners at points A, B, and C. Side AB has a length of #44 #. The distance between the intersection of point A's angle bisector with side BC and point B is #24 #. If side AC has a length of #32 #, what is the length of side BC?

Using, reverse compodundo, #(AB)/(AB+AC)=(BD)/(BD+DC)=(BD)/( BC).#

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To find the length of side BC, we can use the angle bisector theorem. According to this theorem, in a triangle, the angle bisector of a vertex divides the opposite side into segments that are proportional to the lengths of the other two sides.

Let's denote the length of BC as ( x ).

According to the angle bisector theorem: [ \frac{AC}{AB} = \frac{BC}{BD} ]

Given:

- ( AB = 44 )
- ( AC = 32 )
- ( BD = 24 )

We can plug in the values: [ \frac{32}{44} = \frac{x}{24} ]

Now, solve for ( x ): [ x = \frac{32}{44} \times 24 ] [ x = \frac{8}{11} \times 24 ] [ x = 17.4545 ]

So, the length of side BC is approximately 17.45 units.

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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.

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.

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.

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