A triangle has corners points A, B, and C. Side AB has a length of $3$ . The distance between the intersection of point A's angle bisector with side BC and point B is $1$ . If side AC has a length of $4$ , what is the length of side BC?

Question

3834 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-11T10:51:30

$7/3$

Drawn Drawn

Given

Construction

Now

Answer 2 · 2016-06-11T13:52:05

$bar(BC)=7/3$

According to the figure attached, using sinus law we have

$1/sin(alpha)=3/sin(beta)$
$x/sin(alpha)=4/sin(pi-beta)=4/sin(beta)$

so we have

${ (sin(beta)=3 sin(alpha)), (x sin(beta) =4 sin(alpha)) :}$

Then we obtain $x = 4/3$ and $bar(BC)=1+x=7/3$

enter image source here

A triangle has corners points A, B, and C. Side AB has a length of 3 3 . The distance between the intersection of point A's angle bisector with side BC and point B is 1 1 . If side AC has a length of 4 4 , what is the length of side BC?