Find BD, if AD = 8 and DC = 10.

Question

carmuz · Answer

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carmuz · Answer

Possible answers: $$a) 6$$$$b) 6\sqrt{2}$$$$c) 4\sqrt{6}$$$$d) 9$$$$e) 9\sqrt{3}$$

cwrw238 · Answer

this one beats me - doesn't seem to be enough information given to solve it.

carmuz · Answer

Thank you anyway, @cwrw238.

anonymous · Answer

cos(2*theta)=CE/BC         
cos (theta)=BC/18=CE/10
=>cos(2*theta)=5/9
From this point on it should be easy and i think the answer is b)

carmuz · Answer

This problem is supposed to be solved using geometry (similarity and some properties of the right triangle), not Trigonometry. Thank you anyway, @huhumu.

xapproachesinfinity · Answer

trig is still geometry my friend and the fact that they give you those angles
means you need to use right triangle trigonometry

xapproachesinfinity · Answer

i would go with what @huhumu did

carmuz · Answer

I found this problem under "Properties of right triangles" in a geometry book. If they give us those angles, is because they want us to use similarity. I tried, and you all tried, so maybe we need to use trig to get the answer.

cwrw238 · Answer

yes - I did'nt think of using trig for some reason - the properties of right angled triangles include the trig ratios. I tried to use similar triangles and pythagoras theorem but to no avail.

carmuz · Answer

Solved. @huhumu was right: the answer is b) Thank you all.