need help with trig question

Question

A Ferris wheel is 50 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. How many minutes of the ride are spent higher than 40 meters above the ground?

Answer 1

Draw it out as we go since this will help, especially if you are a visual learner.

Where is 40 meters above the ground on the circle of the Ferris wheel? The bottom of the circle is 4 meters above the ground and the center of the circle is 25 meters (half the diameter) above that. So the center of the circle is 29 meters above the ground, leaving 11 meters left for our threshold.

Now we need a right triangle. The hypotenuse is the radius of the circle (25 meters) and the height is our missing altitude (11 meters). Since the question is how many minutes are spent above this threshold and we know the speed of rotation, we need to know the angle of this triangle.

sin(θ)=11 meters/25 meters=26.1 degrees

The target altitude is reached when 26.1 degrees above the center of the circle on the left and again on the right. So the portion of the circle above our threshold is: 180 degrees (the top half of the circle) - 26.1 degrees (left) - 26.1 degrees (right). This leaves 127.8 degrees.

The wheel rotates 360 degrees in 4 minutes. so we'll use a proportion: 127.8 / 360 = x / 4.

And x = ?...