Question

A triangle has corners at points A, B, and C. Side AB has a length of `15`. 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 `33`, what is the length of side BC?

Answer 1

38.4

Explanation:

Here is a sketch (not to scale)

To calculate the length of BC we require to find the length of DC

To do this use the`color(blue)" Angle bisector theorem"`

For the triangle ABC given this is.

`color(red)(|bar(ul(color(white)(a/a)color(black)((BD)/(DC)=(AB)/(AC))color(white)(a/a)|)))`

Substitute the appropriate values into the ratio

`rArr12/(DC)=15/33`

now cross-multiply

`rArr15xxDC=33xx12rArrDC=(33xx12)/15=26.4`

Thus length of BC = BD + DC = 12 + 26.4 = 38.4