Question 1206589

Heron's formula is 

{{{A=sqrt(s(s-a)(s-b)(s-c))}}} , 

where {{{A}}} is the area, {{{s}}} is the semi-perimeter, and {{{a}}}, {{{b}}}, and {{{c}}} are the sides of the triangle.

{{{s=(a+b+c)/2}}}

given:

{{{A = 79}}}°,{{{ b = 73}}}, {{{c = 41}}}


find site {{{a}}} using The Law of Cosines


{{{cos(A) = (b^2 + c^2 - a^2)/( 2bc )}}}

{{{cos(79) = (73^2 + 41^2 - a^2)/( 2*73*41 )}}}

{{{cos(79) = (7010 - a^2)/ 5986 }}}

{{{5986*0.19080899537654492 = 7010 - a^2 }}}

{{{1142.182646324= 7010 - a^2}}} 

{{{a^2=7010 -1142.182646324}}}

{{{a^2=5867.817353676}}}

{{{a=sqrt(5867.817353676)}}}

{{{a=76.6}}}


{{{s=(76.6+73+41)/2}}}

{{{s=95.3}}}


{{{A=sqrt(95.3(95.3-76.6)(95.3-73)(95.3-41))}}}

{{{A=1468.99}}}

{{{A=1469}}}