My Math Forum Problem About Using Cosine Theorem
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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: 7,407 Thanks: 859 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^2-2*a*b*cosC (5x)^2=(7x)^2+(8x)^2-2*7x*8x*cosC 25x^2=49x^2+64x^2-112x^2cosC 25=113-112cosC 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: 2,298 Thanks: 1129 smallest angle is C ... $\cos{C} = \dfrac{7^2+8^2-5^2}{2 \cdot 7 \cdot 8} = \dfrac{11}{14}$ largest angle is B ... $\cos{B} = \dfrac{7^2+5^2-8^2}{2 \cdot 7 \cdot 5} = \dfrac{1}{7}$
 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: 2,298 Thanks: 1129 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: 16,595 Thanks: 1199 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

 Tags cosine, problem, theorem

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