1. ## Triangle - Urgent

In a triangle ABC, X is a point on AC such that AX = 15m, XC = 5m, <AXB = 60 degrees and <ABC = 120 degrees. Find the length of BC.

2. Hello, coatsy!

In $\Delta ABC,\:X$ is a point on $AC$ such that:
. . $AX = 15\,m,\,XC = 5\,m,\;\angle AXB = 60^o,\;\angle ABC = 120^o$
Find the length of BC.
Code:
              B
*
* * *
*   *   *
*     *     *
*       *       *
*         *         *
*           *           *
*         60° * 120°        *
* * * * * * * * * * * * * * * * *
A      15       X       5       C

Since $\angle AXB = 60^o,\;\angle CXB = 120^o$

$\Delta ABC$ has $\angle ABC = 120^o$ and $\angle C$
$\Delta CXB$ has $\angle CXB = 120^o$ and $\angle C$
. . Hence: . $\Delta ABC \sim \Delta CXB$

We have: . $\frac{BC}{20} \,=\,\frac{5}{BC}\quad\Rightarrow\quad BC^2 \,=\,100\quad\Rightarrow\quad\boxed{BC \,=\,10}

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