University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.11 - Linearization and Differentials - Exercises - Page 199: 54


The change in the angle of elevation when a 4% error occurs is less than 0.01 radians ($\approx0.57^\circ$) from $75^\circ$

Work Step by Step

The given height of the building is h and the distance from the point on the ground is 30 ft. change in height(dh): $\frac{dh}{h}$ is less than 4% $\theta =75^\circ$ angle of elevation so $h=30\tan\theta$ so $\frac{dh}{h}=\frac{30\sec^2{\theta}d\theta}{30\tan\theta}$ $0.04\lt\frac{30\sec^2{75}d\theta}{30\tan75}$ $0.01\lt d\theta$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.