Trigonometry » Gradient and angle of elevation


When you have an slope/incline, you always have a horizontal and a vertical shift/translocation. A certain height will be gained over a certain distance.

Right-angled triangle that shows the gradient as the height divided by the distance.
gradient = height

Angle of elevation

The angle that the incline makes with the ground is called the angle of elevation.
See the drawing above.


Instead of gradient, you can also say tangent.
The two expressions below mean the same thing.
- The gradient of 31° is rounded to one decimal 0.6
- The tangent of 31° is rounded to one decimal 0.6

The second expression is in mathematical language:
tan(31°) ≈ 0.6

Now you know this, you can make calculations between the angle and the gradient.
With this gradient, you can calculate unknown sides in the triangle.

See the theory for the tangent.