Answer:
Option (A)
Step-by-step explanation:
It has been given in this question that sign telling path has a 2% grade.
2% grade means a rise of 2 meters for a horizontal change of 100 m (As given in the figure attached).
All the trigonometric ratios for the angle θ between the path and the horizontal are,
Sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
Since measures of the opposite side and adjacent sides are given
Therefore, tangent ratio will be applied to get the measure of the angle,
tanθ = [tex]\frac{2}{100}[/tex]
θ = [tex]\text{tan}^{-1}(\frac{2}{100})[/tex]
Option (A) will be the answer.
