# A triangle has corners at points A, B, and C. Side AB has a length of #21 #. 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 #18 #, what is the length of side BC?

Let D be the point on BC where the angle bisector, intersects with BC

Then BC = BD+ CD

We know that BD = 5 and have to find CD

Substituting known values into this equation.

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

Using the Angle Bisector Theorem, we can determine the length of side BC. The theorem states that in a triangle, if an angle bisector intersects the opposite side, it divides that side into segments proportional to the lengths of the adjacent sides.

Let ( D ) be the point where the angle bisector of angle ( A ) intersects side ( BC ). According to the theorem:

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

Given ( AB = 21 ) and ( AC = 18 ), we can substitute these values:

[ \frac{BD}{CD} = \frac{21}{18} ]

Now, we can solve for ( BD ) and ( CD ):

[ BD = \frac{21}{18} \cdot CD ]

[ CD = \frac{18}{21} \cdot BD ]

We're also given that the distance between ( D ) and ( B ) is ( 5 ). So, we can write:

[ BD - CD = 5 ]

Substitute the expressions for ( BD ) and ( CD ):

[ \frac{21}{18} \cdot CD - CD = 5 ]

[ \left(\frac{21}{18} - 1\right) \cdot CD = 5 ]

[ \frac{3}{18} \cdot CD = 5 ]

[ \frac{1}{6} \cdot CD = 5 ]

[ CD = 5 \times 6 ]

[ CD = 30 ]

Since ( CD ) represents the length of side ( BC ), ( BC = CD = 30 ).

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.

- A triangle has corners at 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 #21 #, what is the length of side BC?
- Triangle A has sides of lengths #51 #, #45 #, and #54 #. Triangle B is similar to triangle A and has a side of length #7 #. 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 #3 #. If side AC has a length of #4 #, what is the length of side BC?
- Can someone help me find the ratio for the sides of this triangle?
- Triangle A has an area of #27 # and two sides of lengths #12 # and #15 #. Triangle B is similar to triangle A and has a side with a length of #25 #. What are the maximum and minimum possible areas of triangle B?

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