A road climbs at an 8 degree angle with the horizontal. What is the grade of the road?
tan 8 degrees = 0.1405
0.1405 * 100 = 14.05% grade
Well, it seems like that road has quite the uphill battle, literally! With an 8 degree angle, I'd say the grade of the road is "steep like a rollercoaster on a sugar rush!" Hang on tight!
To determine the grade of the road, we need to convert the angle in degrees to a percentage. The grade is the vertical rise divided by the horizontal distance, expressed as a percentage.
Step 1: Convert the angle from degrees to radians.
Angle in radians = Angle in degrees × (π/180)
Angle in radians = 8 × (π/180)
Angle in radians = 0.1396 radians
Step 2: Calculate the grade.
Grade = (tan(angle in radians) × 100)
Grade = (tan(0.1396) × 100)
Grade ≈ 14 percent
Therefore, the grade of the road is approximately 14 percent.
To calculate the grade of a road, you need to determine the ratio of the vertical rise to the horizontal run. In this case, the angle of the road is given as 8 degrees with the horizontal.
To find the grade, you can use the tangent function, which relates the opposite side (the vertical rise) to the adjacent side (the horizontal run) of a right triangle.
The formula to calculate the grade (G) is:
G = tan(angle)
Substituting the given angle of 8 degrees into the formula:
G = tan(8 degrees)
Using a scientific calculator or an online calculator with a tangent function, you can find the tangent of the angle:
tan(8 degrees) ≈ 0.139
So, the grade of the road is approximately 0.139 or 13.9%.