The angle of inclination of a road is often expressed as percent grade, which is the vertical rise divided by the horizontal run (expressed as a percent). A 8 % grade corresponds to a road that rises 8 ft for every 100 ft along the horizontal. Find the angle of inclination that corresponds to a 8 % grade. Round your answer to the nearest minute.
\theta =tan^-1(.08)= 4.57 degree
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You're welcome! But let me tell you a little secret - I'm not the most reliable when it comes to math calculations. Also, I'm more inclined (pun intended) to make jokes than provide accurate answers. So, if you're looking for a humorous response, here it goes:
Ah, the angle of inclination! It's like the road is on a never-ending quest to reach for the sky. Well, in this case, an 8% grade means the road is feeling about 4.57 degrees of inclination. Just imagine the road saying, "I've got a slight tilt, but hey, it adds some excitement to the journey!" Keep on rolling, my friend, but stay on the right angle!
To find the angle of inclination that corresponds to an 8% grade, we need to convert the percent grade to a decimal.
The percent grade is given as 8%, which can be written as 0.08 as a decimal.
Now we can use the inverse tangent function (tan^-1) to find the angle of inclination.
θ = tan^-1(0.08)
Using a calculator, we find that the angle of inclination is approximately 4.57 degrees.
Rounding to the nearest minute, the angle of inclination is 4 degrees and 34 minutes.
Therefore, the angle of inclination that corresponds to an 8% grade is approximately 4 degrees 34 minutes.
To find the angle of inclination that corresponds to an 8% grade, you correctly used the tangent function. However, there is a small error in your calculation. Let me show you the correct steps.
The formula to calculate the angle of inclination in degrees using the tangent function is:
θ = tan^(-1)(rise/run)
Here, the rise is 8 ft and the run is 100 ft. So, substituting these values into the formula, we have:
θ = tan^(-1)(8/100)
To evaluate this expression, divide 8 by 100:
θ = tan^(-1)(0.08)
Now, you can use a calculator to find the inverse tangent (also known as arctan) of 0.08. When you calculate it correctly, you get approximately 4.57 degrees.
However, the question asks for the angle of inclination rounded to the nearest minute. To convert from degrees to minutes, there are 60 minutes in one degree. Therefore, multiplying 4.57 degrees by 60 gives you approximately 274.2 minutes.
Rounding this value to the nearest minute, the angle of inclination that corresponds to an 8% grade is approximately 274 minutes.
So, the correct answer to the question is 274 minutes.