# A triangle has corners at points A, B, and C. Side AB has a length of #15 #. The distance between the intersection of point A's angle bisector with side BC and point B is #12 #. If side AC has a length of #36 #, what is the length of side BC?

Length of side BC = 40.8

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

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40.8

I may have misinterpreted the question, but using the wonderful power of MS Paint:

Let D be the point at which the bisector of A meets BC.

Let

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from the sine rule in

from

From the graph

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Using the Angle Bisector Theorem, we can determine the length of side BC.

The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides.

Let D be the point where the angle bisector from A intersects side BC.

According to the theorem: BD/DC = AB/AC

Substitute the given values: 12/(BC - 12) = 15/36

Cross multiply and solve for BC: 12 * 36 = 15 * (BC - 12) 432 = 15BC - 180 15BC = 612 BC = 612/15 BC = 40.8

Therefore, the length of side BC is approximately 40.8.

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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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