Question 1029872
So in other words, the sum of the squares of the legs has to equal 37 using the Pythagorean theorem.
There's only one pair, {{{12}}} and {{{35}}}, since {{{12^2+35^2=37^2}}}.
So then, the smallest angle of this triangle occurs where,
{{{sin(theta)=12/37}}}
{{{cos(theta)=35/37}}}
So then,
{{{sec(theta)=37/35}}}
and the sum is,
{{{S=sin(theta)+sec(theta)}}}
{{{S=12/37+37/35}}}
{{{S=420/(35*37)+1369/(35*37)}}}
{{{S=1789/1295}}}