Question 928855

1.

{{{a=68}}}, {{{B=75}}}°  => {{{A=90-75=15}}}

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

{{{cos(angle)= adjacent_ leg/hypotenuse}}}


In this case we have:

{{{cos(beta)=a/c}}}

After substituting {{{beta=75}}}° and {{{a=68}}} we have:
{{{cos(75)=68/c}}}
{{{c=68/cos(75)}}}
{{{c=68/0.2588}}}
{{{c=262.73}}}

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

{{{b^2=262.73^2-68^2}}}

{{{b^2=69027-4624}}}

{{{b^2=64403}}}

{{{b=253.78}}}


2.

 {{{b = 42}}}, {{{c = 80}}}

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

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

{{{a^2=80^2-42^2}}}

{{{a^2=6400-1764}}}

{{{a^2=4636}}}

{{{a=68.09}}}


3. {{{B = 15}}} degree, {{{b = 52}}}

 To find side {{{a}}} we can use the definition:

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

In this case we have:

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

After substituting {{{beta=15}}}°  and {{{b=52}}} we have:

{{{tan(15)=52/a}}}

{{{a=52/tan(15)}}}

{{{a=52/0.2679}}}

{{{a=194.07}}}

now we can find {{{c}}}

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

{{{c^2=(194.07)^2+52^2}}}

{{{c^2=37663+2704}}}

{{{c^2=40367}}}

{{{c=200.9}}}




4. {{{A = 75}}} degree, {{{a = 126}}}

to find side {{{b}}} use :

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

{{{tan(75)=126/b}}}

{{{b=126/tan(75)}}}

{{{b=126/3.73}}}

{{{b=33.8}}}

now find {{{c}}}:

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

{{{c^2=126^2+(33.8)^2}}}

{{{c^2=15876+1142.44}}}

{{{c^2=17018.44}}}

{{{c=130.5}}}