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?

Answer 1

Caroline Aucoin

#18.1333#

Angle-bisector theorem : #(BD)/(AB)=(DC)/(AC)#

Given that #BD=8, AB=15, AC=19#
#=> 8/15=(DC)/19#
#=> DC=8xx19/15=10.1333#

Hence, length of #BC = BD+DC=8+10.1333=18.1333#

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Answer 2

Sophia Alfred

To find the length of side BC, we can use the angle bisector theorem. According to the theorem, in a triangle, the length of the side opposite to the angle bisector is proportional to the lengths of the other two sides.

Let D be the point where the angle bisector from A intersects side BC. Since the angle bisector divides side BC into segments in proportion to the lengths of the adjacent sides, we have:

BD / DC = AB / AC

Given that AB = 15, AC = 19, and BD = 8 (as given in the problem), we can solve for DC:

BD / DC = AB / AC

8 / DC = 15 / 19

Cross-multiplying, we get:

8 * 19 = 15 * DC

DC = (8 * 19) / 15

DC = 152 / 15

DC = 10.1333 (approximately)

Now, we know the length of DC. To find the length of BC, we add BD and DC:

BC = BD + DC

BC = 8 + 10.1333

BC ≈ 18.1333

So, the length of side BC is approximately 18.1333.

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Answer from HIX Tutor

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