# A triangle has corners at points A, B, and C. Side AB has a length of #27 #. The distance between the intersection of point A's angle bisector with side BC and point B is #18 #. If side AC has a length of #36 #, what is the length of side BC?

Length of BC = 42

Let the point where the angle bisector intersects with side BC be D

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Using the Angle Bisector Theorem, we can find the length of side BC. The theorem states that in a triangle, if an angle bisector intersects the opposite side, it divides that side into segments proportional to the lengths of the other two sides.

Let ( D ) be the intersection point of the angle bisector of angle ( A ) with side ( BC ). According to the Angle Bisector Theorem:

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

Given that ( AB = 27 ), ( AC = 36 ), and ( BD = 18 ) (as mentioned in the question), we can plug these values into the equation:

[ \frac{18}{DC} = \frac{27}{36} ]

Solving for ( DC ):

[ DC = \frac{36 \times 18}{27} = 24 ]

Now, since ( BD = 18 ) and ( DC = 24 ), the length of side ( BC ) is the sum of these lengths:

[ BC = BD + DC = 18 + 24 = 42 ]

Therefore, the length of side ( BC ) is 42 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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