Question 1080836

 How many triangles can be formed if side {{{a = 29ft}}}? 

In triangle {{{ABC}}}, < {{{A = 60}}}°, and side {{{c = 18ft}}}. 


{{{a/sin(A)=c/sin(C)}}}

{{{29/sin(60)=18/sin(C)}}}

{{{29/(sqrt(3)/2)=18/sin(C)}}}

{{{29sin(C)=18(sqrt(3)/2)}}}

{{{sin(C)=15.5884572681/29}}}

{{{sin(C)=0.5375330092}}}

{{{C=sin^-1(0.5375330092)}}}

< {{{ C=32.52}}}°

< {{{B=180-(60+32.52)=180-92.52=87.48}}}°


{{{b/sin(B)=a/sin(A)}}}

{{{b/sin(87.48)=29/sin(60)}}}

{{{b/0.9990329=33.48631561}}}

{{{b=33.48631561*0.9990329}}}

{{{b=33.45ft}}}

so, there is only {{{one}}} triangle that could be formed.