Question 1150839
{{{drawing ( 600, 600, -10, 15, -10, 10,

circle(0,5,.12),locate(0.5,5.5,A),circle(10,0.12),locate(10,-0.5,B),blue(line(0,5,10,0)),blue(line(0,5,15,5)),locate(1.5,4.7,47),locate(8.5,0.5,47),circle(4,0,.12),locate(4,-0.5,C),locate(2,-0.5,4mil),blue(line(4,0,4,5)),blue(line(10,0,4,5)),locate(5,4.5,62),locate(7,1.5,62),locate(7,-0.5,x),locate(3.5,2.5,h),locate(0.5,2.5,h),locate(4,5.5,D),
graph( 600, 600, -10, 15, -10, 10, 0)) }}} 

from triangle AOB we have:

{{{tan(47)=h/4}}}

=> {{{h=4tan(47)}}}.....eq.1


from triangle CDB we have:

{{{tan(62)=h/x}}}

=> {{{h=x*tan(62)}}}.....eq.2


from eq.1 and eq.2 we have

{{{4tan(47)=x*tan(62)}}}

{{{x=4tan(47)/tan(62)}}}

{{{x=4(1.07236871)/1.880726465346332}}}

{{{x=2.28mil}}}