Expert: Abe Mantell - 1/9/2009

Question
I have a Trig question. Since I graduated 30 years ago, I cant remember how to do this. Everyday I walk on a treadmill 1& 1/2 miles at an incline or angle of 12 degrees. I want to know what the total elevation (opposite side) was that I walked. Again, the angle is 12 degrees and the total adjacent side or length is 7920 feet. Please showe me how to figure the answer so I can determine different figures later as I continue to increase the angle or distance. Thanks in advance.


Answer
Hello Brian,

All you need to know is right triangle trig...the mnemonic SohCahToa.
Since you know the angle (12 deg), adjacent side and want the opposite,
we'll use Tangent (as the "Toa" reminds us that Tangent(angle)=opp/adj).
Thus... tan(12 degrees)=x/7920, where x is the vertical displacement.
Solving for x gives: x=7920tan(12 degrees) or about 1683.4 ft.

OK?

Abe