A wheelchair ramp has a rise from the ground of 1 foot. The ramp has a length of 14 feet. To the nearest degree, find the angle the ramp makes with the sidewalk.
slope=tangent(θ)=rise/run=1/14
θ=atan(1/14)=4° approx.
To find the angle the ramp makes with the sidewalk, we can use trigonometry. The angle can be determined using the tangent function, which is defined as the ratio of the rise to the run.
In this case, the rise of the ramp is 1 foot, and the length (or run) of the ramp is 14 feet.
The tangent of an angle theta is given by the formula:
tan(theta) = rise / run
Substituting the values, we get:
tan(theta) = 1 / 14
Now, to find the angle theta, we can use the inverse tangent function (also known as arctangent or atan). The arctangent of both sides of the equation cancels out the tangent, resulting in:
theta = arctan(1 / 14)
Using a calculator, we find that arctan(1 / 14) is approximately 3.6 degrees.
Therefore, to the nearest degree, the angle the ramp makes with the sidewalk is 4 degrees.
To find the angle the ramp makes with the sidewalk, we can use trigonometry. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side of a right triangle.
In this case, the opposite side is the height of the ramp (1 foot) and the adjacent side is the length of the ramp (14 feet). Therefore, the tangent of the angle is given by:
tan(angle) = opposite/adjacent
tan(angle) = 1/14
Now, to find the angle, we can take the inverse tangent (also known as the arctan) of both sides of the equation. This will give us:
angle = arctan(tan(angle))
angle = arctan(1/14)
Using a scientific calculator, we can find the approximate value of the arctan(1/14) to the nearest degree.
The result is approximately 3.61 degrees.
Therefore, to the nearest degree, the angle the ramp makes with the sidewalk is 4 degrees.