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
5 answers
Which side is the hypotenuse? We can't see your "figure below".
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.
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
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
drwls your answer seems very confusing isnt there a simpiler way to solve this????
Fjjf
1 answer