an isosceles triangle on the coordinate plane has side lengths of 8,5,and 5 units. The long side is along the x-acis, find the coordinates of each vertex.

Answer 1

place the long side on the x-axis so that it runs from
(0,0) to (8,0)
then the altitude cuts the base in half and hits it at (4,0)
looks like we have 2 right-angled triangles with base of 4 and hypotenuse of 5,
by Pythagoras that height has to be 3
(s^2 + 4^2 = 5^2)

so the third vertex must be (4,3)