A road has a 10% grade (slope). To the nearest degree what is the angle of elevation of the road?
How long of a climb, short climb, steeper. Long climb, not as steep!
Review what the grade is. It just means that
tanθ = 0.1
5.7 degrees
To find the angle of elevation of the road, we can use the trigonometric relationship involving the slope or grade of the road.
The grade of the road can be expressed as a percentage, which represents the vertical change (rise) over the horizontal distance (run) multiplied by 100. In this case, the grade is given as 10%.
To find the angle of elevation, we can use the arctangent function. The arctangent of the grade in decimal form (0.1 in this case) will give us the angle of elevation in radians. To convert the angle from radians to degrees, we can multiply it by 180/π (approximately 57.3 degrees).
So, the steps to find the angle of elevation are as follows:
1. Convert the grade from a percentage to a decimal by dividing it by 100.
10% = 10/100 = 0.1
2. Find the arctangent of the decimal.
arctan(0.1)
3. Convert the angle from radians to degrees by multiplying it by 180/π.
arctan(0.1) * (180/π)
Calculating the above expression gives us approximately 5.71 degrees.
Therefore, the angle of elevation of the road, to the nearest degree, is 6 degrees.