a sign on a straight stretch of freeway reads, 9% grade, altitude 3000 feet. What is the angle of the road?
what is math to u!!!!!!!!!!!!!!!!
What is the length if the width is:3.1. The area is 31mi.2. I realy need the answer.
To find the angle of the road given the grade and altitude, we need to understand what a 9% grade means.
A 9% grade indicates that for every 100 units of horizontal distance traveled, there is a vertical increase or decrease of 9 units.
In this case, the altitude is given as 3000 feet. This means that when we travel 100 units horizontally, the road will have risen or descended by 9% of those 100 units, which is 9 units.
To find the angle, we can use the trigonometric relationship between the angle, the vertical distance traveled, and the horizontal distance traveled.
We can consider the altitude gained (9% of 100) as the opposite side of a right triangle, and the 100 units of horizontal distance as the adjacent side.
The tangent of the angle is equal to the ratio of the altitude gained to the horizontal distance. So, in this case, the tangent of the angle can be expressed as 9/100.
Using inverse tangent (arctan), we can find the angle:
angle = arctan(9/100)
Calculating this equation, the angle of the road would be approximately 5.144 degrees.