Question

A hill that has a 12.0% grade is one that rises 12.0 m vertically for every 100.0 m of distance in the horizontal direction. At what angle is such hill inclined above the horizontal

Answer 1

Answer on Question #45583, Physics, Mechanics | Kinematics | Dynamics

A hill that has a $12.0\%$ grade is one that rises $12.0\mathrm{m}$ vertically for every $100.0\mathrm{m}$ of distance in the horizontal direction. At what angle is such hill inclined above the horizontal?

Solution:

We use the tangent ratio

$$\tan \theta = \frac {\text {o p p o s i t e}}{\text {a d j a n c e n t}} = \frac {1 2}{1 0 0} = 0. 1 2$$

Thus,

$$\theta = \tan^ {- 1} (0. 1 2) = 6. 8 4 3 {}^ {\circ}$$

Answer: $\theta = 6.843{}^{\circ}$

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