Since the centre is 105 m above the ground,

k = 105

(k is the vertical shift of the centre point from the horizontal x-axis)

Since the radius of the wheel is 75 m,

a = 75

(a is the amplitude, or the distance between the highest point and the centre point)

Since it takes 30 minutes to complete one cycle,

Period = 30 minutes

b = Frequency,
b = 2pi / 30
b = pi/15

So, y = 105 + 75 sin (pi/15 t)

When the visitor is 150 m above ground.

105 + 75 sin (pi/15 t) = 150
75 sin (pi/15 t) = 45
sin (pi/15 t) = 3/5

Basic angle = sininv (3/5) = 0.6435011088 rad

t = first quadrant OR second quadrant
t = basic OR pi - basic
t = 0.6435... - 2.498...

So, the person would be 150 m above the ground at times t = 0.64 s amd t = 2.50 s.