Question 929644
given:the right triangle

{{{a= 3.0}}}

{{{A=alpha= 31.0}}}°=> {{{B=beta= 90-31.0}}}°=> {{{beta= 59.0}}}°

to find side {{{b}}} we can use the definition:

{{{tan(angle)=opposite_leg/adjacent_leg}}}

In this case we have:

{{{tan(alpha)=a/b}}}

After substituting {{{alpha=31}}} and {{{a=3}}} we have:

{{{tan(31)=3/b}}}

{{{b=3/tan(31)

{{{b=3/0.6009}}}

{{{b=4.99}}}

and, now we can use Pythagorean theorem to find side {{{c}}}


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

{{{c^2=3^2+(4.99)^2}}}

{{{c^2=9+24.9}}}

{{{c^2=33.9}}}

{{{c=sqrt(33.9)}}}

{{{c=5.82}}}