This is a triangle with the ground and the pole as legs, and the view line as hypotenuse. Calculate the pole height h using the sine rule. The angles of the triangle are 90, 60 and 30 (sum must be 180).
The sine rule says that h/sin(60) = 150/sin(30), so h = 150*sin(60)/sin(30) ≈ 259.8
