SOLUTION: Given: SSA triangle, A={{{ 31 }}}°, a={{{ 22 }}}cm, b={{{ 9 }}}cm. Find B, C & c A.) 17.3; 131.7; 21.3cm B.) 17.3; 131.7; 26.7cm C.) 12.2; 136.8; 29.2cm D.) 12.2; 136.8;

Algebra ->  Test -> SOLUTION: Given: SSA triangle, A={{{ 31 }}}°, a={{{ 22 }}}cm, b={{{ 9 }}}cm. Find B, C & c A.) 17.3; 131.7; 21.3cm B.) 17.3; 131.7; 26.7cm C.) 12.2; 136.8; 29.2cm D.) 12.2; 136.8;       Log On


   

Question 1068552: Given: SSA triangle, A=+31+°, a=+22+cm, b=+9+cm.
Find B, C & c
A.) 17.3; 131.7; 21.3cm
B.) 17.3; 131.7; 26.7cm
C.) 12.2; 136.8; 29.2cm
D.) 12.2; 136.8; 21.3cm.
Thanks.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Since side b is so much shorter than side a,
the angle opposite b (angle B)
must be a lot smaller than A (the angle opposite side a).
Even if B was the same as A,
the two of them would add to just 62%5Eo ,
showing you that angle C must be larger than
180%5Eo-62%5Eo=118%5Eo .
Angle C and side c must be really large,
certainly larger than A and a,
so you know that choices A and D are wrong,
and you would be betting for answer C.

If thou are not pressed for time,
you can calculate rather than bet,
just in case the answer is B.

We use law of sines, which says
sin%28A%29%2Fa=sin%28B%29%2Fb=sin%28C%29%2Fc ,
and also makes it true that
c%2Fsin%28C%29=a%2Fsin%28A%29=b%2Fsin%28B%29 .
sin%28B%29=b%2Asin%28A%29%2Fa=9%2A0.515038%2F22=0.210697
B=sin%5E%28-1%29%280.210697%29--->highlight%28B=12.16%5Eo%29 .
Now that we know the measures of angles A and B ,
C=180%5Eo-%2831%5Eo%2B12.16%5Eo%29=180%5Eo-43.16%5Eo .
So, highlight%28C=136.84%5Eo%29 .
Finally,
c%2Fsin%28C%29=a%2Fsin%28A%29 , so
c=a%2Asin%28C%29%2Fsin%28A%29=22%2A0.684079%2F0.515038---->highlight%28c=29.2%29 .