The road rose at an 8 degree angle, what is the grade?
slope or grade is the same as the tangent of the angle
so tan 8°= ??
To determine the grade of a road, you need to calculate the rise over run, expressed as a percentage. The rise refers to the vertical change, while the run represents the horizontal distance.
In this case, we know that the road rose at an 8-degree angle. To calculate the grade, we can use the tangent function, which relates the angle to the rise and run. The formula to find the tangent of an angle is:
Tangent(angle) = rise / run
Since the rise is not given, we need to introduce a reference horizontal distance for the run. For simplicity, let's assume the reference run is 100 units. This choice is arbitrary and doesn't affect the resulting grade.
Now, we can calculate the rise using the tangent formula:
Tangent(8 degrees) = rise / 100
To isolate the rise, multiply both sides of the equation by 100:
rise = Tangent(8 degrees) * 100
Using a scientific calculator or approximation, let's find the tangent of 8 degrees:
Tangent(8 degrees) ≈ 0.1405
Now, substitute this value back into the formula to calculate the rise:
rise ≈ 0.1405 * 100
rise ≈ 14.05 units
So, the rise of the road is approximately 14.05 units for every 100 units of horizontal distance. To express this as a percentage, divide the rise by the run and multiply by 100:
grade = (rise / run) * 100
grade ≈ (14.05 / 100) * 100
grade ≈ 14.05%
Therefore, the grade of the road is approximately 14.05%.