A man observes that when he has walked $c$ metres up an incline, the angular depression of an object in a horizontal plane through the foot of the slope is $\alpha$, and that when he has walked a further distance of $c$ metres the depression is $\beta$.then the inclination of the slope to the horizon is the angle whose cotangent is $\left( 4\cot { \alpha } -\cot { \beta } \right)$.

Using trigonometric modeling for the inclined plane, the horizontal distances to the object correspond to the depression angles and the walked distances. By formulating the height and horizontal base equations, the cotangent of the angle of inclination evaluates to 3 cot alpha minus cot beta. Since this coefficient is 3 rather than 4, the provided statement is false.

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