If there are 4 lines having inclinations 45∘,60∘,120∘ and 135∘.Find the line having greatest slope and steepest slope?
Steepest or greatest slope is one and the same. These are two different ways of understanding slope.
The degree of slope i.e. greatest or smallest is denoted by absolute value of gradient.Gradient is given by tan of angle.
In our case, the angles are 45∘,60∘,120∘ and 135∘. Out of these, both tangent of both the angles 60∘ and 120∘ have the same value = 1.732. Hence, the lines having angles 60∘ and 60∘ are steepest among the given lines.