Question 313335
{{{tan(A)=sin(A)/cos(A)}}}
{{{sin(A)=4/R}}}
{{{cos(A)=3/R}}}
{{{sin^2(A)+cos^2(A)=1}}}
{{{16/R^2+9/R^2=1}}}
{{{25/R^2=1}}}
{{{R^2=25}}}
{{{R=5}}}
{{{sin(A)=4/5}}}
{{{cos(A)=3/5}}}
Similarly for {{{B}}},
{{{144/R^2+25/R^2=1}}}
{{{169/R^2=1}}}
{{{R=13}}}
{{{sin(B)=12/13}}}
{{{cos(B)=5/13}}}
Use the trig identity,
{{{cos(A-B)=cos(A)cos(B)+sin(A)sin(B)}}}
{{{cos(A-B)=(3/5)(5/13)+(4/5)(12/13) }}}
{{{cos(A-B)=(15/65)+(48/65) }}}
{{{cos(A-B)=63/65}}}