A hill in the Tour de France bike race has a grade of 8%. To the nearest degree, what is the angle that this hill makes with the horizontal ground? Round to the nearest tenth of a degree.
(Hint: An 8% grade means an 8-foot rise over 100 horizontal feet. First sketch this problem and decide which inverse trigonometric ratio to use to find the unknown angle.)

Question

A hill in the Tour de France bike race has a grade of 8%. To the nearest degree, what is the angle that this hill makes with the horizontal ground? Round to the nearest tenth of a degree. 
(Hint: An 8% grade means an 8-foot rise over 100 horizontal feet. First sketch this problem and decide which inverse trigonometric ratio to use to find the unknown angle.)

paxpolaris · Answer

(Hint: An 8% grade means an 8-foot rise over 100 horizontal feet. ...

paxpolaris · Answer

First sketch this problem|dw:1413527931659:dw|

paxpolaris · Answer

|dw:1413527994948:dw|

looks like:$$\large \tan(x)={8\over100}$$

paxpolaris · Answer

$$\implies \tan(x)=0.08$$

$$\Large x=\tan^{-1}(0.08)$$... (remember to use calculator in degree mode.)