The slope of a ramp leading into a grocery store is 1:6. What is the angle of elevation of the ramp?
Well, if we're talking about a ramp into a grocery store, we better make sure it's not a joke! The slope 1:6 means that for every 1 unit of vertical rise, there are 6 units of horizontal run. To find the angle of elevation, we can use some math. Let's just say that this ramp is not too steep, but it's also not flat like a pancake. It's just right, like Goldilocks' porridge! So, grab your math hat and get ready for some calculations. We can start by finding the tangent of the angle of elevation. The tangent of an angle is equal to the ratio of the vertical rise (1) over the horizontal run (6). So, the tangent of the angle of elevation is 1/6. Now, we can use the inverse tangent function (aka arctan) to find the angle itself. Punching in those numbers on our trusty calculators, we get approximately 9.5 degrees. Ta-da! That's the angle of elevation of the ramp. Just remember to hold onto your grocery cart tightly, or you might find yourself sliding down the ramp with your groceries in tow!
To find the angle of elevation of the ramp, we can use the formula:
Angle of elevation = arctan(slope)
Given that the slope of the ramp is 1:6, we convert it to decimal form by dividing 1 by 6:
slope = 1/6 = 0.1667
Now, we can find the angle of elevation using the formula:
Angle of elevation = arctan(0.1667)
Using a calculator or trigonometric table, we find that the angle of elevation is approximately 9.47 degrees.
To find the angle of elevation of the ramp, we can use the inverse tangent function. The slope of the ramp, given as 1:6, means that for every 1 unit of vertical rise, there are 6 units of horizontal run.
We can represent this slope as the ratio of the opposite side (vertical rise) to the adjacent side (horizontal run) in a right triangle.
Let's label the angle of elevation as θ. Using the inverse tangent function (tan^(-1)), we can write the equation:
tan(θ) = opposite/adjacent = 1/6
Now, we can solve for θ by taking the inverse tangent of both sides:
θ = tan^(-1)(1/6)
Using a scientific calculator, we can find the angle of elevation to be approximately 9.47 degrees.
Therefore, the angle of elevation of the ramp leading into the grocery store is approximately 9.47 degrees.
Slope = Tan A = Y/X = 1/6
A = 9.46o