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

Length of side BC = 10.3333

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

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To find the length of side BC in the triangle with corners at points A, B, and C, where 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 5, and side AC has a length of 16:

Let's denote the length of side BC as ( x ).

Using the Angle Bisector Theorem, we know that the angle bisector of angle A divides side BC into segments proportional to the other two sides of the triangle. Therefore, we can set up the following proportion:

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

Plugging in the given values, we have:

[ \frac{15}{16} = \frac{x}{x + 5} ]

Cross-multiplying yields:

[ 15(x + 5) = 16x ]

Expand and solve for ( x ):

[ 15x + 75 = 16x ] [ 75 = 16x - 15x ] [ 75 = x ]

So, the length of side BC is 75 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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- Please solve q 60 ?

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