Question 1121779


the right triangle given that:

{{{ m}}} < {{{A=30}}} degrees, 

{{{m}}} < {{{C=90}}} degrees, and 

{{{a=15}}}

since the sum of all angles in triangle is {{{180}}}, we have


{{{m}}} < {{{B= 180-(90+30)}}}

{{{m}}} < {{{B= 180-120}}}

{{{m}}} < {{{B= 60)}}} degrees

since  {{{m}}} < {{{A=30}}} degrees  side and {{{a=15}}} ,use sin theorem to calculate hypotenuse {{{c}}} 

{{{sin(30)=a/c}}}

{{{1/2=15/c}}}

{{{(1/2)c=15}}}

{{{c=30}}}


and, now use Pythagorean theorem to fond side  {{{b}}}

{{{b^2=c^2-a^2}}}

{{{b^2=30^2-15^2}}}

{{{b^2=900-225}}}

{{{b^2=675}}}

{{{b=sqrt(675)}}}

{{{b=25.98076211353316}}}

or approximately

{{{b=25.9}}}