The needle of a dip circle shows an apparent dip of `45^@` in a particular position and `53^@` when the circle is rotated through `90^@`. Find the true dip.

Explanation

If `delta_(1) and delta_(2)` be the apparent dips shown by the dip circle in the 2 perperdicular positions the true dip `delta` is diven by
`cot^(2) delta = cot^(2) delta_(1) + cot^(2)delta_(2)`
`rArr cot^(2) delta = cot^(2)45^(@) + cot^(2)53^(@)`
`cot^(2)delta = 1.56`
`cot^(2)delta = 1.56`
`delta = 38.6^(@) = 39^(@)