If a ferris wheel has a radius of 20.5meters, how tall would a 45 degree angle be?
sin45 = height/20.5
height = 20.5sin45 = 14.4 m above the axle
To determine the height of the ferris wheel at a 45 degree angle, we need to use the trigonometric function sine.
The sine function relates the length of the side opposite an angle to the length of the hypotenuse in a right triangle. In this case, the radius of the ferris wheel forms the hypotenuse, and the height we want to find is the side opposite the 45 degree angle.
Using the definition of sine, which states that sin(angle) = opposite/hypotenuse, we can rearrange the equation to solve for the opposite side:
opposite = sin(angle) * hypotenuse
In this case, the angle is 45 degrees and the hypotenuse is the radius of the ferris wheel, which is 20.5 meters.
Therefore, the height of the ferris wheel at a 45 degree angle can be calculated as follows:
height = sin(45 degrees) * 20.5 meters
Now, let's calculate it:
height = sin(45 degrees) * 20.5 meters
Using a scientific calculator or an online trigonometry calculator, we find that sin(45 degrees) is equal to approximately 0.7071.
Plugging in this value:
height = 0.7071 * 20.5 meters
height ≈ 14.49 meters
So, the height of the ferris wheel at a 45 degree angle would be approximately 14.49 meters.