Angle of an inclined plane

Statement

An inclined plane has a gradient of $25\%$ (that is, $25$ cm of rise for every $100$ cm horizontally). Compute the angle of inclination.

Solution

The gradient is the ratio of vertical rise to horizontal run, that is the tangent of the angle of inclination $\theta$: $\tan\theta = \frac{25}{100} = 0{,}25 \;\Rightarrow\; \theta = \arctan(0{,}25) \approx \boxed{14{,}04°}.$

Links

Topics: Goniometry
Concepts: Arctangent · Tangent
Functions: Arctangent · Inverse trigonometric functions
Skills: Modelling · Using formulae
Exercise types: Word problem