Question

A preprogrammed workout on a treadmill consists of intervals walking at various rates and angles of incline. A 1% incline means 1 unit of vertical rise for every 100 units of horizontal run. At what angle, with respect to the horizontal, is the treadmill bed when set at a 10% incline?

Answer 1

The angle of a treadmill bed set at a 10% incline with respect to the horizontal can be found by taking the arctan of 0.10, resulting in approximately 5.71 degrees.

Step-by-step explanation:

The student asked at what angle, with respect to the horizontal, is the treadmill bed when set at a 10% incline. A 10% incline means that for every 100 units of horizontal distance, there is a 10-unit vertical rise. To calculate the angle of the incline (θ), we use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle.

Here is the step by step calculation:

Write down the definition of the tangent of an angle, which is tan(θ) = opposite / adjacent.

In this scenario, the opposite side is the vertical rise, and the adjacent side is the horizontal run. So, tan(θ) = 10 / 100 = 0.10.

To find the angle θ, we take the arctangent (inverse tangent) of 0.10: θ = arctan(0.10).

Use a calculator to find θ, which will give us the angle in degrees.

Therefore, the angle θ of the treadmill bed with respect to the horizontal when set at a 10% incline can be found by calculating arctan(0.10), which is approximately 5.71 degrees.