let

a = the length of the base

h = the length of the altitude

The ratio of the base of an isosceles triangle to its altitude is 3:4

a : h = 3 : 4 cross multiply

4a = 3h

h = (4/3)a

let

A is the measure of each angle that lies on the base

B is the third angle

tan A = h/(a/2)

plug h = (4/3)a into the last equation

tan A = ((4/3)a)/(a/2)

tan A = 8/3

A = arctan 8/3

A = 69.44 degrees

since 2A + B = 180

B = 180 - 2A

B = 180 - 2*69.44

B = 41.12 degrees

the measures of the angles in the triangle are 69.44 degrees and 41.12 degrees.