A Ferris wheel is 200 feet in diameter and makes on revolution every 60 seconds. For how many seconds of any revolution is your seat above 150 feet? You must justify your answer with appropriate explanations, calculations, and a diagram.

Step 1 ：The Ferris wheel is a circle with a diameter of 200 feet, so the radius is 100 feet. When the seat is above 150 feet, it means the vertical distance from the center of the Ferris wheel to the seat is more than 50 feet. This forms a right triangle with the radius and the horizontal line from the center to the vertical line of the seat.

Step 2 ：We can use trigonometric functions to calculate the angle corresponding to the seat being above 150 feet. The cosine of this angle is equal to the vertical distance divided by the radius, or \(\cos(\theta) = \frac{50}{100} = 0.5\). Therefore, \(\theta = \cos^{-1}(0.5) = 60^\circ\).

Step 3 ：However, the seat is above 150 feet for both the ascent and the descent of the Ferris wheel, so the total angle for which the seat is above 150 feet is \(2 \times 60^\circ = 120^\circ\).

Step 4 ：The Ferris wheel makes one revolution every 60 seconds, so the time corresponding to an angle of \(\theta\) degrees is \(\frac{\theta}{360} \times 60\) seconds. Therefore, the time for which the seat is above 150 feet is \(\frac{120}{360} \times 60 = 20\) seconds.

Step 5 ：Final Answer: The seat is above 150 feet for \(\boxed{20}\) seconds of any revolution.