In the diagram below of right triangle ACB, altitude CD intersects AB at D. If AD=3 and DB=4, find the length of CD in simplest radical form.

How do I go about figuring out this problem?
Please help. thanks

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  1. Which side is the hypotenuse? We can't see your "figure below".

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  2. The hypotenuse is side AB, or side ADB. The altitude goes from the vertex angle C down to point D, which is between A and B.

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  3. let x be the angle ACD, part of the right angle at C. 90-x is then angle DCB.

    You know that
    CD tan x = 3 and
    CD tan (90-x) = CD cot x = 4
    Divide one equation by the other and the CD cancels out
    tanx/cotx = tan^2 x = 3/4
    tanx = (sqrt3)/2

    CD = 3/tanx = 3*2/(sqrt3) = 2 sqrt3

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  4. drwls your answer seems very confusing isnt there a simpiler way to solve this????

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