P is PD, vertical AB and vertical foot is D. According to the meaning of the question, PD= 1.

Calculating AC from Cosine Theorem

AC^2=AB^2+BC^2-2AB*BC*COS30

= 10^2+(4√3)^2-2* 10*4√3*√3/2

=28

AC =2√7

According to sine theorem:

BC/sinA=AC/sinB

sinA=BC*sinB/AC

=( 10* 1/2)/2√7

=5√7/ 14

In the right triangle APD (D is the vertical foot),

Sine of a = opposite side/adjacent side = 1/AP=5√7/ 14.

So AP=2√7/5

So CP=AC-AP

=2√7-2√7/5

=8√7/5