Question 1206928


1. {{{A = 15}}}° and {{{c = 37}}}

{{{ drawing( 600, 600, -10, 10, -10, 10,
blue(line(1,0.1, 7,0.1)),
blue(line(7,5, 7,0.1)),
blue(line(1,0.1, 7,5)),
locate(1.5,0.6,15), locate(3.5,3.5,37),
locate(0.5,-0.5,A),locate(7,-0.5,C),locate(07,5.5,B),
graph( 600, 600, -10, 10, -10, 10, 0)) }}}


we know that  < {{{C=90}}}°

 find angle {{{B}}}

< {{{B=90-15=75}}}°

use the law of sine to find side{{{ b}}}

{{{c/sin(C)=b/sin(B)}}}

{{{37/sin(90)=b/sin(75)}}}

{{{37/1=b/sin(75)}}}

{{{b=37*sin(75)}}}

{{{b=35.74}}}


find side {{{a }}}

{{{a/sin(15)=35.74/sin(75)}}}

{{{a=sin(15)(35.74/sin(75))}}}

{{{a=9.58}}}



2. {{{B = 64}}}° and {{{c = 19.2}}}

{{{ drawing( 600, 600, -10, 10, -10, 10,
blue(line(1,0.1, 7,0.1)),
blue(line(7,5, 7,0.1)),
blue(line(1,0.1, 7,5)),
locate(6.5,4.6,64), locate(3.5,3.5,19.2),
locate(0.5,-0.5,A),locate(7,-0.5,C),locate(7,5.5,B),
graph( 600, 600, -10, 10, -10, 10, 0)) }}}


< {{{C=90}}}°

< {{{A=90-64=26}}}°

{{{19.2/sin(90)=b/sin(64)}}}

{{{b=19.2*sin(64)}}}

{{{b=17.26}}}

{{{a/sin(26)=17.26/sin(64)}}}

{{{a=sin(26)(17.26/sin(64))}}}

{{{a=8.42}}}



3. {{{A = 15}}}° and {{{c = 25}}}

sketch it yourself as I did above


< {{{C=90}}}°

< {{{B=90-15=75}}}°

{{{a/sin(15)=25/sin(90)}}}

{{{a=25*sin(15)}}}

{{{a=6.47}}}


{{{b/sin(75)=25/sin(90)}}}

{{{b=25*sin(75)}}}

{{{b=24.15}}}



4. {{{A = 45}}}° and {{{c = 16}}}


< {{{C=90}}}°

< {{{B=90-45=45}}}°

since < {{{A}}}= < {{{B}}}, than side {{{a=b}}}


{{{a/sin(45)=16/sin(90)}}}

{{{a=16*sin(45)}}}

{{{a=11.3}}}
{{{b=11.3}}}


5. {{{B = 56}}}° and {{{c = 16}}}

< {{{C=90}}}°

< {{{A=90-56=34}}}°


{{{b/sin(56)=16/sin(90)}}}

{{{b=16*sin(56)}}}

{{{b=13.26}}}


{{{a/sin(34)=16/sin(90)}}}

{{{a=16*sin(34)}}}

{{{a=8.95}}}