The height would be 3.7
Because it's an isosceles triangle, you and I know that the sides are 4 and the base is 3. We also know that to find the height we need to use Pythagorean's theorem. Therefore, h square + 1.5 square = 4 square (we get 1.5 from dividing 3 to get the base). Solve it and the height is 3.7