Question

let ABC be a right angled triangle with BC=3 and AC=4. let D be a point on the hypotenuse AB such that angle BCD=30 degrees. the length of CD is

Answer 1

If C is the right angle, then AB=5.

Drop an altitude from D to BC, meeting it at E.

Then, if DE=x, CD=2x and EB = 3/4 x.

So,

(3 - 3x/4)^2 + x^2 = (2x)^2
x = (16√3-12)/13

and CD=2x.