# A triangle has corners at points A, B, and C. Side AB has a length of #32 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #28 #, what is the length of side BC?

Referencing the attached figure, we have two triangles

but

Dividing term to term the two equations we have

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Using the Angle Bisector Theorem, the length of side BC can be found using the formula:

[ \frac{AB}{AC} = \frac{BD}{DC} ]

Given: [ AB = 32 ] [ AC = 28 ] [ BD = 4 ]

Substituting the given values: [ \frac{32}{28} = \frac{4}{DC} ]

Solving for DC: [ DC = \frac{28 \times 4}{32} = 3.5 ]

So, the length of side BC is 3.5.

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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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