# A triangle has corners points A, B, and C. Side AB has a length of #9 #. The distance between the intersection of point A's angle bisector with side BC and point B is #6 #. If side AC has a length of #14 #, what is the length of side BC?

The length of

And

Therefore,

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 an angle in a triangle 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 problem, AD is the angle bisector and BD is given as 6 units.

We know that the ratio of BD to DC should be the same as the ratio of AB to AC:

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

Given that AB = 9 and AC = 14, we can substitute these values into the equation:

[ \frac{6}{DC} = \frac{9}{14} ]

Cross multiplying gives:

[ 6 \times 14 = 9 \times DC ]

[ 84 = 9 \times DC ]

[ DC = \frac{84}{9} ]

[ DC = 9.33 ]

So, the length of side BC is the sum of BD and DC:

[ BC = BD + DC ]

[ BC = 6 + 9.33 ]

[ BC = 15.33 ]

Therefore, the length of side BC is approximately 15.33 units.

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.

- Triangle A has sides of lengths #28 #, #36 #, and #24 #. Triangle B is similar to triangle A and has a side of length #8 #. What are the possible lengths of the other two sides of triangle B?
- A baker is serving a new circular brownie pizza dessert (1" thick with a volume of 132.25 cubic inches). What are the dimensions of the open-topped cardboard box needed to serve the brownie pizza (assume the brownie to be inscribed in the box)?
- Britney is 5 feet tall and casts a 3 1/2 -foot shadow at 10:00 A.M. At that time, a nearby tree casts a 17-foot shadow. Two hours later, Britney's shadow is 2 feet long. What is the length of the shadow of the tree at this time?
- 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 #24 #, what is the length of side BC?
- Given the figure determine the value of the unknown segment, #x#?

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