Question

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 `16`, what is the length of side BC?

Answer 1

BC ≈ 8.81

Explanation:

Firstly, let the point where the angle bisector intersects with side BC be D.

Then by the `color(blue)" Angle bisector theorem "`

`(BD)/(DC) = (AB)/(AC)`

Require to find DC.

Substitute the appropriate values into the ratio to obtain.

`rArr 5/(DC) = 21/16`

Now cross-multiply : `21xxDC = 16xx5`

To obtain DC , divide both sides by 21

`rArr (cancel(21) DC)/cancel(21) = (16xx5)/21`

`rArr DC ≈ 3.81`

Now , BC = BD + DC = 5 + 3.81 = 8.81 to 2 decimal places.