# 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 #16 #. If side AC has a length of #28 #, what is the length of side BC?

30

Firstly , let the point where the angle bisector intersects with side BC be D.

Require to find DC.

Substitute the appropriate values into the ratio to obtain.

To obtain DC , divide both sides by 32

Now , BC = BD + DC = 16 + 14 = 30

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Using the Angle Bisector Theorem, we can determine that the length of side BC can be found using the proportion:

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

Given that AC = 28 and AB = 32, and letting x represent the length of BC, we can set up the proportion:

[\frac{28}{32} = \frac{28-x}{16}]

Solving this equation will give us the length of BC:

[28 \times 16 = 32 \times (28-x)] [448 = 896 - 32x] [32x = 896 - 448] [32x = 448] [x = \frac{448}{32}] [x = 14]

So, the length of side BC is 14 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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