The slope of a ramp leading into a grocery store is 3:16. What is the angle of elevation of the ramp?
To find the angle of elevation of the ramp, we need to determine the tangent of the angle.
Tangent (tan) is defined as the ratio of the opposite side to the adjacent side of a right triangle.
In this case, the opposite side represents the vertical change or rise of the ramp, and the adjacent side represents the horizontal change or length of the ramp.
Given that the slope of the ramp is 3:16, the ratio of the rise to the length is 3/16.
Let's assume the rise of the ramp is 3x, and the length of the ramp is 16x.
Now we can write the equation:
tan(angle) = rise/length
tan(angle) = 3x / 16x
tan(angle) = 3/16
Now we need to find the angle whose tangent is 3/16.
Using the inverse tangent function (tan^(-1)), we can find the angle:
angle = tan^(-1)(3/16)
Using a calculator, the angle is approximately 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 tangent function.
1. First, we need to find the value of the slope of the ramp as a decimal. The slope ratio given is 3:16. To convert this to a decimal, divide 3 by 16:
Slope = 3 ÷ 16 = 0.1875
2. Now, we can use the tangent function to find the angle of elevation. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the slope (0.1875) and the adjacent side is 1 (since it is the horizontal distance).
tan(angle) = slope
tan(angle) = 0.1875
3. To find the angle itself, we can take the inverse tangent (also known as arctan or tan^(-1)) of both sides:
angle = arctan(0.1875)
Using a calculator or math software, we can find the angle to be approximately 10.63 degrees.
Therefore, the angle of elevation of the ramp is approximately 10.63 degrees.
To find the angle of elevation of the ramp, we can use the slope formula. The slope is defined as the change in vertical distance divided by the change in horizontal distance. In this case, the slope is given as 3:16, which means for every 3 units of vertical rise, there are 16 units of horizontal run.
The slope formula is:
slope = vertical rise / horizontal run
Since the slope is given as 3:16, we can assign 3 units to the vertical rise and 16 units to the horizontal run. So, the slope is:
slope = 3 / 16
To find the angle of elevation, we can use the inverse tangent function (tan⁻¹) of the slope. In other words, we need to take the arctan of the slope:
angle of elevation = tan⁻¹(slope)
Using a scientific calculator or the trigonometric functions available in many programming languages, we can calculate the angle of elevation by plugging in the slope:
angle of elevation = tan⁻¹(3 / 16)
Approximately, the angle of elevation of the ramp is 10.61 degrees.