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

 

We can find an acute triangle with the three altitude lengths 1, 2, and h, if and only if h^2 belongs to interval (p,q) Find (p,q).

 Feb 2, 2019
 #1
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If the third side = 17....we have a right triangle

 

So...the greatest integer length of remaining side  is 16

 

And because of the triangle inequality

 

8 + unknown side > 15

 

unknown side > 7

 

So....the possible integer lengths are  [ 8 , 16 ]

 

cool cool cool 

 Feb 2, 2019

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