+27 An acute triangles two sides measure 8 and 15. How many possible lengths are there for the third side if it is an integer?
+129850 Using the Triangle Inequality we have that
8 + 15 > x
23 > x
Also
8 + x > 15
x > 7
So.....the unknown side x can be
7 < x < 23
And there are 15 integers between 7 and 23
+27 The answer is wrong because it has to be an acute triangle. Most of the 15 integers make the triangle an obtuse angle.
+129850 Thanks....I missed the "acute" part
The triangle will be obtuse if this is true
missing side > sqrt ( 15^2 + 8^2)
missing side > sqrt (289)
missing side > 17
And when x = 17...we have a right triangle
So.... the triangle will be acute when x = 8, 9, 10, 11, 12, 13, 14, 15, 16
So....9 values are possible for an acute triangle
