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 Oran2009 June 13th, 2016 06:46 PM

Geometry Triangle Question

1. In the triangle shown, $n$ is a positive integer, and $\angle A > \angle B > \angle C$. How many possible values of $n$ are there?

http://i1175.photobucket.com/albums/...ps8bv8ybhe.png

2. Two sides of an acute triangle are 8 and 15. How many possible lengths are there for the third side, if it is a positive integer?

 skeeter June 13th, 2016 07:29 PM

1). $\angle B > \angle C \implies 3n+1 > 4n-9 \implies n < 10$

Triangle inequality ... $7n-8 > 3n+4 \implies n > 3$

conclusion?

2). If 8 and 15 are the two shorter sides and x is the longest side, then $8^2+15^2 > x^2 \implies x < 17$

If 8 and x are the two shorter sides and 15 is the longest side, then $8^2+x^2 > 15^2 \implies x > \sqrt{161} \approx 12.7$

conclusion?

 Oran2009 June 13th, 2016 07:42 PM

But #2 says it is a positive integer

 Cartesius24 June 14th, 2016 12:26 AM

And it shows possible values.

 skeeter June 14th, 2016 05:42 AM

Quote:
 Originally Posted by Oran2009 (Post 539204) But #2 says it is a positive integer
How many positive integers are within the interval $\sqrt{161} < x < 17$ ?

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