Question

Help solving for X

Answer 1

Don't know how to set it up

Answer 2

its a similar concept foor setting it up.

Answer 3

not quite.

AB BC
-- = ----
AD CD

can you find what AD is? and then plug in numbers or varibale to the corresponding lengths and you should ahve your proportion

Answer 4

close. look carefully
AD is not 58. AC is 58

Answer 5

so
33 54
--- = ---
58-x x

Answer 6

cross multiply

33x= 58-x(54)
and solve for x

Answer 7

You use the angle bisector theorem

http://www.mathwarehouse.com/geometry/similar/triangles/angle-bisector-theorem.php

which is how nikato was able to set up the proportion. Solving for x does give you x = 36. So you are correct.

Answer 8

First I find the angle, \(\theta\) using the Law of Cosines:
$$
54^2+33^2-2\times54\times33\cos2\theta=x^2\\
\implies \theta=\cfrac{1}{2}\cos^{-1}\cfrac{541}{3564}\approx 0.695\\
$$
http://en.wikipedia.org/wiki/Law_of_cosines
Then I use the law of cosines again with this angle \(\theta\) to find x. I let \(BD=y\):
$$
54^2+y^2-2\times54\times y\cos \theta=x^2\\
33^2+y^2-2\times33\times y\cos \theta=(58-x)^2\\
\implies x=36
$$
Using Wolfram as my calculator to solve these two equations for x:
http://www.wolframalpha.com/input/?i=t%3D%281%2F2%29acos%28641%2F3564%29%2C54^2%2By^2-2*54*y*cos%28t%29%3Dx^2%2C33^2%2By^2-2*33*y*cos%28t%29%3D%2858-x%29^2

The bisector theorem as suggested by @jim_thompson5910 is likely much easier.