Question

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

Answer 1

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

Answer 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.

Answer 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

Answer 4

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

Answer 5

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