SOLUTION: The lengths of the sides of ABC are 9.5, 12.8, and 13.7. (a) To the nearest hundredth of a degree, the measure of the smallest angle in the triangle is .

Algebra ->  Trigonometry-basics -> SOLUTION: The lengths of the sides of ABC are 9.5, 12.8, and 13.7. (a) To the nearest hundredth of a degree, the measure of the smallest angle in the triangle is .      Log On


   

Question 288700: The lengths of the sides of ABC are 9.5, 12.8, and 13.7.
(a) To the nearest hundredth of a degree, the measure of the smallest angle in the triangle is .
Answer by texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
What grade is this? Have you seen the Cosine Law before?

The Cosine Law is:
c%5E2=a%5E2%2Bb%5E2-2abCos%280%29

To find the smallest angle, o, we need to use c as the smallest side, 9.5. Plug the numbers in with a=12.8, b=13.7 and c=9.5, then solve for the angle, o.

%289.5%29%5E2=%2812.8%29%5E2%2B%2813.7%29%5E2-2%2812.8%29%2813.7%29Cos%28o%29

Rearrange this equation to find:
Cos%28o%29+=+-261.28%2F-350.72
o=41.84 degrees

If you need any clarifications about steps in this problem, let me know!