Question

As you are walking down a path, you see a sign telling the path has a 2% grade (ie., a rise of 2 metres for a horizontal change of 100m). Which of the following expressions will calculate the angle between the path and horizontal?

Answer 1

Option (A)

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 =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

Cosθ =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

tanθ =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

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 =
`(2)/(100)`

θ =
`\text{tan}^(-1)((2)/(100))`

Option (A) will be the answer.