# Thread: Using trig to find a sidelength?

1. ## Using trig to find a sidelength?

In a triangle ABC, X is a point on AC so that (AX/XC) = 3 and angle AXB = 70 degrees. Find the length of AC if angle ABC = 110 degrees and BC = 6 cm

I don't know if this fits under trigonometry or geometry, but it is a triangle. My teacher has hinted that similar triangles may be involved. Thanks to anyone who helps.

2. ## ..

<XCB=<BCA
<BXC=<ABC
Hence triangles ABC & XBC are similar
so
AB/XB= BC/XC = AC/BC

BC^2=AC*XC...(1)
now
AC/XC=4/1
=>AC/4=XC
so
put XC in (1)
u get (AC^2)/4=36
hence AC=12