Question 1177586



recall:
Sine Function:
{{{sin(a) = Opposite / Hypotenuse}}}
Cosine Function:
{{{cos(a) = Adjacent / Hypotenuse}}}
Tangent Function:
{{{tan(a) = Opposite / Adjacent}}}


given {{{tan(a)=2/5}}} =>{{{opp=2}}} and {{{adj=5}}}

find hypothenuse

{{{hyp^2=opp^2+adj^2}}}

{{{hyp^2=2^2+5^2}}}

{{{hyp=sqrt(4+25)}}}

{{{hyp=sqrt(29)}}}
 

{{{sin(a)=2/sqrt(29)}}} or {{{sin(a)=-2/sqrt(29)}}}


since given angle is in quadrant {{{III}}} , sin  is {{{negative}}}, so use

{{{sin(a)=-2/sqrt(29)}}}