A triangle has corners at points A, B, and C. Side AB has a length of #16 #. 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 #8 #, what is the length of side BC?

Answer 1

Length of side BC = 18

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

#"using the "color(blue)"angle bisector theorem"#
#(AB)/(AC)=(BD)/(DC)#
#16 / 8 = 12 / (DC)#
#DC = (12*8) / 16 = 6#
#BC = BD+DC= 12+6 =18#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

Using the Angle Bisector Theorem, we can find the length of side BC. The 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 of angle A intersects side BC.

According to the theorem, we have:

BD / DC = AB / AC

Given that AB = 16 and AC = 8, we can substitute these values into the equation:

BD / DC = 16 / 8 BD / DC = 2

Since BD + DC = BC, we can represent BD as 2x and DC as x:

2x + x = BC 3x = BC

Now, we know that the distance between the intersection of the angle bisector and point B is 12. This distance is the sum of BD and the length from the intersection to point B. Since BD is 2x, the length from the intersection to point B is x. Therefore:

2x + x = 12 3x = 12 x = 4

Now, we can find the length of BC:

BC = 3x BC = 3 * 4 BC = 12

So, the length of side BC is 12.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7