Hello, VonNemo19!

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: .

Hence: .

We are given: . . (Angles are in.)radians

Therefore: .

The maximum error is: .