Question 1004205


 use hint "draw the altitude from y" 

let the altitude be {{{x}}}, then from first right angle triangle we have

{{{sin(30)=x/16}}}
{{{1/2=x/16}}}
{{{(1/2)16=x}}}
{{{x=8}}}

let angle at {{{Z}}} be {{{theta}}}

{{{sin(theta)=x/24}}}....since {{{x=8}}}

{{{sin(theta)=8/24}}}

{{{sin(theta)=1/3}}}

{{{theta=19.5}}}


since angle {{{Y}}} is divided in two angles by altitude, let them be {{{alpha}}} and {{{beta}}}, 

so,{{{Y=alpha+beta}}}

{{{alpha}}} is in first right angle triangle where is angle of {{{30}}} degrees, so {{{alpha=60}}} degrees

in second right angle triangle, one angle is {{{theta=19.5}}}, and {{{beta=70.5}}}

now we have angle {{{Y=60+70.5}}}=>{{{Y=130.5}}}

side {{{y}}} is divided by altitude into {{{a}}} and {{{b}}}
since we know all angles and two sides in each right angle triangle, we can find {{{a}}} and {{{b}}}

{{{cos(30)=a/16}}}

{{{a=sqrt(3)/2*16}}}

{{{a=sqrt(3)*8}}}

{{{a=13.85640646055102}}}

{{{a=13.9}}}


{{{cos(19.5)=b/24}}}

{{{b=0.795815*24}}}

{{{b=22.6}}}


{{{y=a+b}}}

{{{y=13.9+22.6}}}

{{{highlight(y=36.5)}}}