A triangle has sides of integer lengths 3, 6 and x. For how many values of x will the triangle be acute?
The triangle will be acute for 3<x<√32+62=3<x<3√5That's a continuum of values so asking how many there are is sort of meaningless
Actually, the answer key says it is 1. Do you know how?
oh it says integer lengths... DOH
3<x<3√5≈6.7That gives you 4, 5, and 6
4 gives you an angle of about 36.36 degrees
5 gives you an angle of about 56.25 degrees
6 gives you an angle of about 75.53 degrees
all 3 are acute triangles
+937 
