Question 868502

Since {{{A}}} and {{{B}}} are complementary,
{{{A+B=90}}}
{{{cos(A+B)=0}}}
But you also know,
{{{cos(A+B)=cos(A)cos(B)-sin(A)sin(B)}}}
{{{cos(A)cos(B)=sin(A)sin(B)}}}
.
.
Since,
{{{cos^2(A)+sin^2(A)=1}}}
{{{25/169+sin^2(A)=1}}}
{{{sin^2(A)=144/169}}}
{{{sin(A)=12/13}}}
.
.
Substituting,
{{{(5/13)cos(B)=(12/13)sin(B)}}
{{{cos(B)=(12/5)sin(B)}}}
You also know that,
{{{cos^2(B)+sin^2(B)=1}}}
{{{(144/25)sin^2(B)+sin^2(B)=1}}}
{{{(169/25)sin^2(B)=1}}}
{{{sin^2(B)=25/169}}}
{{{highlight(sin(B)=5/13)}}}