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? Please Help. I tried using triangle inequality, but I got nowhere... 
1). $\angle B > \angle C \implies 3n+1 > 4n9 \implies n < 10$ Triangle inequality ... $7n8 > 3n+4 \implies n > 3$ 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? 
But #2 says it is a positive integer 
And it shows possible values. 
Quote:

All times are GMT 8. The time now is 11:03 PM. 
Copyright © 2018 My Math Forum. All rights reserved.