angle of elevation

Question

A person starts out 17 miles from the base of a tall mountain, and looks up at a 4 degree angle of elevation to the top of the mountain. When they move 12 miles closer to the base of the mountain, what will be their angle of elevation when they look to the top?

Answer 1

The Formula for Tangent, if referring to "SOHCAHTOA" is Opposite/Adjacent.

 

When drawing this kind of problem, it should look like a right triangle with the base of 17 mi, going up from one end to the other at 4 degrees (doesn't have to be drawn to scale). x should represent the vertical side (i.e. the mountain height).

You would use the formula of Tangent to Get: Tan (4^o) = x/17. (Opposite of the Angle/Adjacent to the Angle). Make sure your calculator is in Degree Mode.

 

After finding x, you would have to use an Inverse Tangent (if on the TI-83/4, it'd be 2nd+Tan).

12 miles closer means the person is 5 miles away now.

Plug in: tan^-1(x/5). x would be the answer you got earlier.

And that should give you the new Angle of Elevation.

 

Hope that helps.