Question

You are designing a ramp where the horizontal distance is twice the vertical rise. what will be the ramp angle to the nearest tenth of a degree?

Answer 1

The angle of a ramp where the horizontal distance is twice the vertical rise is approximately 26.6 degrees to the nearest tenth of a degree, calculated using the inverse tangent function of the ratio between the rise and run.

Step-by-step explanation:

To find the angle of a ramp where the horizontal distance is twice the vertical rise, we can use trigonometry. Specifically, we can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. In this scenario, the vertical rise is the opposite side, and the horizontal distance, being twice the vertical rise, is the adjacent side.

The formula we will use is:

tan(θ) = opposite / adjacent

Let's denote the vertical rise as 'h' and the horizontal distance as '2h'. Plugging these into the formula gives us:

tan(θ) = h / (2h) = 1 / 2

Now, we use the inverse tangent function (arctan) to find θ:

θ = arctan(1/2)

Using a calculator:

θ ≈ 26.565 degrees

To the nearest tenth of a degree:

θ ≈ 26.6 degrees

This means the ramp angle is approximately 26.6 degrees to the nearest tenth of a degree.

Answer 2

use the definition of tangent

or inv tangent (arctan or atan)

tan(theta) = opposite side/ adjacent side

the vertical rise would be the opposite side, the horozontal distance would be the adjacent side

let rise = y
let distance= x
x=2y

so tan(theta) = y/2y
tan(theta) = 1/2

theta = atan(1/2)

grab a handy dandy calculator, unless you know this conversion off the top of your head