# A triangle has corners at points A, B, and C. Side AB has a length of #8 #. 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 #9 #, what is the length of side BC?

Angle bisector of an angle in a triangle divides the opposite side in the ratio of its adjacent sides.

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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.

- 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 #8 #. If side AC has a length of #19 #, what is the length of side BC?
- Triangle A has an area of #6 # and two sides of lengths #5 # and #7 #. Triangle B is similar to triangle A and has a side with a length of #19 #. What are the maximum and minimum possible areas of triangle B?
- A triangle has corners at points A, B, and C. Side AB has a length of #12 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #21 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #48 #. 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 #24 #, what is the length of side BC?
- At the same time of day, a man who is 57.6 inches tall casts a 49.2-inch shadow and his son casts a 41-inch shadow. How do you use similar triangles to determine the height of the man's son?

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