The slope leading into a grocery store is 3:16 what is the angle of the elevation of the ramp?
To find the angle of elevation of the ramp, we can use the slope ratio of 3:16.
The slope ratio represents the change in height (rise) compared to the change in distance (run). In this case, for every 3 units of height, there are 16 units of distance.
The tangent function can be used to find the angle of elevation. The tangent of an angle is defined as the opposite over the adjacent.
In this case, the opposite side is the height (rise) and the adjacent side is the distance (run).
Let's assume the height of the ramp is 3x and the distance is 16x (where x is any constant).
The tangent of the angle can be calculated as:
tan(angle) = rise / run = 3x / 16x = 3/16
Now, we can find the angle by taking the arctan of both sides:
angle = arctan(3/16)
Using a calculator, we find that angle ≈ 10.6 degrees.
Therefore, the angle of elevation of the ramp is approximately 10.6 degrees.
To find the angle of elevation of the ramp, we can use the inverse tangent function. The slope of the ramp is given as 3:16.
To convert this slope to a ratio, we can divide both numbers by their greatest common divisor. In this case, the greatest common divisor is 1. So, the slope can be expressed as 3/16.
The tangent of an angle is calculated by dividing the length of the side opposite the angle by the length of the side adjacent to the angle. In this case, the opposite side is the rise of the ramp (3 units) and the adjacent side is the run of the ramp (16 units).
Using the formula for tangent, we have:
tan(θ) = opposite/adjacent = 3/16
Now, we can find the angle by taking the inverse tangent (arctan) of 3/16:
θ = arctan(3/16)
Using a calculator, the angle of elevation of the ramp is approximately 10.6 degrees (rounded to one decimal place).
Therefore, the angle of elevation of the ramp is approximately 10.6 degrees.
To find the angle of elevation of the ramp, we can use the inverse tangent function.
The slope is given as the ratio of the rise (vertical change) to the run (horizontal change), which is 3:16. This means that for every 3 units in vertical change, there are 16 units in horizontal change.
Let's assume that the angle of elevation is represented by θ.
Therefore, we have the following equation:
tan(θ) = rise/run
We can substitute the given values:
tan(θ) = 3/16
To find the value of θ, we need to take the inverse tangent (arctan) of both sides:
θ = arctan(3/16)
Using a scientific calculator or an online calculator, we can evaluate arctan(3/16) to find the angle of elevation.
The angle of elevation can be expressed in degrees or radians, depending on the calculator setting. Make sure to verify the correct unit when obtaining the result.