A road has a steady gradient of 1 in 10. What angle does the road make with the horizontal? Give your answer to the nearest degree.
Gradient is the ratio of height over the horizontal distance.
A gradient of 1 in 10 means that for every 10 meter of horizontal movement we go by a height of one meter.
We measure the gradient as the tangent of an angle. The angles are measured in degrees or radians. The tagent ratio of an angle ina right angled triangle is the ratio of the opposite side to the adjascent side of the angle.
Thus if the section has the gradient of 1/10, it is equivalent to thetangent ratio of angle A of a right angled triangle whose right angle making sides are AB= 10 and BC = 1.
Therefore, by trigonometry, tanA = 1/10.
Or angle = arc tangent (1/10).
Therefore x = 5.7106 degree nearly (by calculator).
Hope this helps.
A gradient of 1 in 10 means that for every 10 units of horizontal distance traverses there is 1 unit of vertical drop or rise. The angle of Tan of this angle (A) of drop or rise with the horizontal can be calculates as:
tan A = (Horizontal Distance)/(Vertical Distance)
Substituting the values of the horizontal and vertical distances as identified:
tan A = 1/10 = 0.1
From trigonometric tables we see that angle corresponding to this value of tan is 5.71 degrees.
A = 6 degrees (Rounded off to nearest degree)
Angle the road makes with horizontal = 6 degrees.