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January 24th, 2017, 07:06 AM  #1 
Newbie Joined: Dec 2016 From: On Planet Earth Posts: 9 Thanks: 0  Problem About Using Cosine Theorem
Find cosine for the lowest and the largest angles in triangle ABC, if AB:BC:AC=5:7:8 I tried to solve using cosine theorem. But I did not get the answer that is given in the book. 
January 24th, 2017, 07:23 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,434 Thanks: 870 Math Focus: Elementary mathematics and beyond 
Will you show your work? What is the book's answer?

January 24th, 2017, 07:44 AM  #3 
Newbie Joined: Dec 2016 From: On Planet Earth Posts: 9 Thanks: 0 
Yeas, of course. c^2=a^2+b^22*a*b*cosC (5x)^2=(7x)^2+(8x)^22*7x*8x*cosC 25x^2=49x^2+64x^2112x^2cosC 25=113112cosC cosC=11/14 The books's answers: 5/6; 0.1 
January 24th, 2017, 08:01 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,422 Thanks: 1189 
smallest angle is C ... $\cos{C} = \dfrac{7^2+8^25^2}{2 \cdot 7 \cdot 8} = \dfrac{11}{14}$ largest angle is B ... $\cos{B} = \dfrac{7^2+5^28^2}{2 \cdot 7 \cdot 5} = \dfrac{1}{7}$ 
January 24th, 2017, 08:36 AM  #5 
Newbie Joined: Dec 2016 From: On Planet Earth Posts: 9 Thanks: 0  skeeter Yeas, these answers are what i got, but in the book they are not the same. Book's answers are: 5/6; 0.1 I can think that the book's answer is not correct. 
January 24th, 2017, 08:45 AM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,422 Thanks: 1189 
book "answers" are not immune to being incorrect ...

January 24th, 2017, 09:14 AM  #7 
Newbie Joined: Dec 2016 From: On Planet Earth Posts: 9 Thanks: 0 
Thank you to all helping me to meditate how wonderful is Mathematics, and how Almighty is The God who created all the lows of Mathematics and not only of Mathematics. I am really happy to be a member of this forum. Great.

January 24th, 2017, 09:33 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 16,775 Thanks: 1234 
It would seem that the problem should give "if AB:BC:AC=5:7:9". Did you misread it?

January 24th, 2017, 09:49 AM  #9 
Newbie Joined: Dec 2016 From: On Planet Earth Posts: 9 Thanks: 0  skipjack No, no. in the book is: 5:7:8 

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