The angle of elevation of the top of a hill is:
and the distance to the top of the hill is: .
Find the maximum error in determining the height of the hill.
So, I let be the distance to the top, be the angle of elevation,
and be the height of the hill, then: .
Now, the total differential is: .
Now what do I do?
Do some math . . . Find ... then substitute the given values.
We have: .
We are given: . . (Angles are in radians.)
The maximum error is: .