Question 1026535
A little bit of algebra steps:
{{{system(x*tan(7)=u,x*tan(35)=d,u+d=14)}}}


{{{system(x=u/tan(7),x=d/tan(35),u+d=14)}}}


{{{u=14-d}}}
Substitute.
{{{system(x=(14-d)/tan(7),x=d/tan(35))}}}


Solve either of those for d.  Choosing the tan(35) equation,
{{{d=x*tan(35)}}}, which we already had formed earlier.
Substitute into the tan(7) equation:
{{{x=(14-(x*tan(35)))/tan(7)}}}


Continue solving for x.
{{{x*tan(7)=14-x*tan(35)}}}
{{{x*tan(7)+x*tan(35)=14}}}
{{{x(tan(7)+tan(35))=14}}}
{{{highlight(x=14/(tan(7)+tan(35)))}}}-----use either table of values or scientific calculator for computing this.


{{{highlight(x=10.4)}}}



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That was question #1.  I did not try question 2.