How many solutions does a triangle with side lengths a=22, A=117 degrees, and b=25 have? Write your answer in numeric form.?

Question

kj4uts · Answer

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anonymous · Answer

Only one solution.

You know the one angle. You know the two side lengths coming from that angle. Thus the end points of the the third side are defined.

A triangle has three angles and three sides. As long as they give you three things, you can solve for the other three. They could give you

SSA (side, side, angle)
SSS
SAA
AAA

Under those conditions, the triangle will always have just one solution.

kj4uts · Answer

It's not 0?

kj4uts · Answer

I am a little confused because I found this: http://openstudy.com/study#/updates/51f9ef0de4b06e6a116f3602

phi · Answer

if angle A is opposite side a  (I assume it is)
then we use this idea:
the biggest angle "goes with" the biggest side  
i.e. if  angle A is the biggest angle,  then its opposite side a is the longest side.

but in your problem side b is longer than side a, which means angle B must be bigger than angle A.  B>117
but if A is 117 and B is bigger, call it 118
they add up to more than 180, and that is not allowed.

so there is no triangle that has those numbers.

kj4uts · Answer

So 0 solutions then?

phi · Answer

yes, 0 solutions.  But learning the logic is more important than the answer.

kj4uts · Answer

Ok thank you for explaining that to me!