SOLUTION: Find the length of AB in the figure. In simplest radical form. https://media.discordapp.net/attachments/769181283913695264/826191575326916678/P3kqRms5H3v3AAAAAElFTkSuQmCC.png

Algebra ->  Triangles -> SOLUTION: Find the length of AB in the figure. In simplest radical form. https://media.discordapp.net/attachments/769181283913695264/826191575326916678/P3kqRms5H3v3AAAAAElFTkSuQmCC.png      Log On


   



Question 1177802: Find the length of AB in the figure.
In simplest radical form.
https://media.discordapp.net/attachments/769181283913695264/826191575326916678/P3kqRms5H3v3AAAAAElFTkSuQmCC.png

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

Let alpha = ∠ABC = ∠DBX
From triangle BAC:
|AB| = +35%2Acos%28alpha%29+ (1)
We also have (from triangle BDC):
cos%282%2Aalpha%29+=+15%2F35+=+3%2F7+
Apply cos%282x%29+=+2cos%5E2%28x%29-1+
+2cos%5E2%28alpha%29-1+=+3%2F7+
...
+cos%28alpha%29+=+sqrt%285%2F7%29+
Now, re-write (1) using this result:
|AB| = +35%2Asqrt%285%2F7%29+ = +highlight%285%2Asqrt%2835%29%29+ cm
(approx. 29.580cm)