# 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 #27 #, what is the length of side BC?

The length of side BC is 26

Let D be the intersection of point A's angle bisector with side BC.

The bisector theorem states that:

Then

that's

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

To find the length of side BC, we can use the angle bisector theorem. According to this theorem, the angle bisector of a triangle divides the opposite side into segments that are proportional to the lengths of the other two sides.

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

Using the angle bisector theorem, we can set up the following proportion:

[\frac{AC}{AB} = \frac{BC}{BC+8}]

Substituting the given values:

[\frac{27}{12} = \frac{x}{x+8}]

Now, we can solve for x:

[27(x + 8) = 12x]

[27x + 216 = 12x]

[27x - 12x = -216]

[15x = -216]

[x = \frac{-216}{15}]

[x = -14.4]

However, the length of a side cannot be negative, so we discard this solution.

Therefore, there might be a mistake in the setup of the problem. Double-checking the given information is recommended.

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

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.

- Given the similar right triangles in the figure. Find the exact values of x and y?
- Suppose triangle ABC ~ triangle GHI with scale factor 3:5, and AB=9, BC=18 and AC=21. What is the perimeter of triangle GHI?
- Triangle A has an area of #24 # and two sides of lengths #8 # and #15 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the maximum and minimum possible areas of triangle B?
- Triangle A has sides of lengths #5 ,4 #, and #8 #. Triangle B is similar to triangle A and has a side of length #1 #. What are the possible lengths of the other two sides of triangle B?
- A triangle has corners at points A, B, and C. Side AB has a length of #6 #. 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 #8 #, what is the length of side BC?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7