SOLUTION: NAME THE LONGEST ANGLE AND THE SMALLEST ANGLE IN THE FF. In triangle ABC, Ab=12, AC=16, BC=9 Thank you :)

Question 840537: NAME THE LONGEST ANGLE AND THE SMALLEST ANGLE IN THE FF.
In triangle ABC, Ab=12, AC=16, BC=9
Thank you :)

Found 2 solutions by jim_thompson5910, thejackal:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The largest angle is always opposite the largest side. The largest side is AC = 16 and the angle opposite this side is angle B. So angle B is the largest angle.

Similarly, the smallest angle is always opposite the smallest side. The smallest side is BC = 9 and the angle opposite this side is angle A. So angle A is the smallest angle.

Summary:

Largest Angle: Angle B

Smallest Angle: Angle A
Answer by thejackal(72) (Show Source): You can put this solution on YOUR website!
i think you mean't name the largest and smallest angle.
nevertheless, an angle of a triangle can be found if only two sides of that angle are known.
that said, the formula you are looking is below:
for our question, lets set a=Ab=12, b=AC=16,c=BC=9
Cos angle A = (b^2+c^2-a^2)/2bc = (256+81-144)/2*16*9 = 193/288 = 0.67013888
Angle A = arccos(cos A) = 47.92221547 degrees
Cos angle B = (a^2+c^2-b^2)/2ac = (144+81-256)/2*12*9 = -31/216 = -0.1435185
Angle B = arccos(cos B) = 98.25149928 degrees
Angle C = 180 - A - B = 33.82628525

(by the way, arccos is simply inverse cosine. You can us your calc for that)

Have a look at this write up for a good reference:
http://en.wikipedia.org/wiki/Solution_of_triangles
http://www.mathsisfun.com/algebra/trig-solving-sss-triangles.html
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