Question

9.Iconstruction In problem 4, topsoil must be bought to cover the sector to a depth of 4 in.How many cubic yards of topsoil are needed? (Be careful with the units.)

Answer 1

The sketch of the question can be shown on a line diagram below

`\begin{gathered} where \\ \theta=gr\text{ adient angle} \\ \text{opposite = 6 ft} \\ \text{adjacent = 82 ft} \end{gathered}`

To get the gradient angle, we make use of the trigonometrical ratio of tan

`\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \tan \theta=(6)/(82) \\ \tan \theta=0.0732 \\ \theta=\tan ^(-1)(0.0732) \\ \theta=4.187^0 \\ \end{gathered}`

Therefore, the gradient angle of the road is 4.19 degrees.