Question 1204461


given:

{{{a=25}}}
{{{c=30}}}
angle {{{B=54}}}°

use the law of  cosine to calculate  side{{{ b}}}

{{{b= sqrt(a^2+c^2-2ac*cos(B))}}}

{{{b= sqrt(25^2+30^2-2*25*30*cos(54))}}}

{{{b= 25.3638}}}


now find angle {{{x}}} (actually angle {{{C}}})


{{{x=cos^-1((a^2+b^2-c^2)/2ab)}}}

{{{x=cos^-1((25^2+25.3638^2-30^2)/(2*25*25.3638))}}}

{{{x=73.1}}}°

third angle is

{{{A=180-(B+x)}}}

{{{A=180-(54+73.1)}}}

{{{A=52.9}}}°


Answer: {{{x=73.1}}}°

complete solution:

Sides:
{{{a = 25}}}
{{{b = 25.3638}}}
{{{c = 30}}}

Angles:
{{{A = 52.9}}} °
{{{B = 54 }}}°
{{{C=x= 73.1}}} °