Question

At a distance of 120ft from the foot of a tower the elevation of its top is 60o. If the possible error in measuring the distance and elevation are 1 inch and 1 minute, find approximate error in calculated height.

(a) 0.342

(b) 0.284

(c) 0.154

(d) 0.986

I got this question in an internship interview.

This key question is from Errors and Approximations topic in chapter Partial Differentiation of Engineering Mathematics

Answer 1

The correct option is (b) 0.284

Explanation: Tan(z) = ^h⁄x

h = x Tan(z)

Taking log and then differentiate we get,

^∂h⁄h = ^∂x⁄x + ^1⁄Tan(z)  Sec^2 (z)δz

Now h = 120 tan(60^o) = 120√3

Putting, δx = ^1⁄12 ft, δz = ^π⁄(60*180)

Putting the values we get,

δh = 0.284.