Asked by Diana
two sides of a triangle measure 8 and 15. how many integer values can be assigned to the third side so that all the angles in the triangle are acute.
Answers
Answered by
Reiny
For all angles to be acute, no single angle can be ≥ 90°
let's assume the angle between the 8 and 15 is 90°
by Pythagoras, the third side would have to be17.
So the largest integer we could have for the third side is 16
But to have a triangle , the sum of any two sides has to be greater than the third side.
let the third side be x
then
x+8 > 15 or x > 7
so possible third sides are
8,9,10,11,12,13,14,15,16 or 9 integer values
let's assume the angle between the 8 and 15 is 90°
by Pythagoras, the third side would have to be17.
So the largest integer we could have for the third side is 16
But to have a triangle , the sum of any two sides has to be greater than the third side.
let the third side be x
then
x+8 > 15 or x > 7
so possible third sides are
8,9,10,11,12,13,14,15,16 or 9 integer values
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