   Chapter 2.9, Problem 36E

Chapter
Section
Textbook Problem

# One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 ° , with a possible error of ± 1 ° .(a) Use differentials to estimate the error in computing the length of the hypotenuse.(b) What is the percentage error?

To determine

a)

To estimate:

The error in computing the length of the hypotenuse by using differential

Explanation

1) Formula:

The power rule combined with the chain rule,

ddxun=n un-1dudx

Let  be the angle and h be the hypotenuse in right angle triangle.

Use sinθ=oppositehypotenuse= 20h

sinθ= 20h

Solve for h

h = 20sinθ

2) Given:

θ=300, b = 20 cm and possible error  θ= ± 10

3) Calculation:

Differentiate h = 20sinθ with respect to 

dhdθ=20 ddθ(sinθ)-1

By using power rule combined with the chain rule,

dhdθ=20  (-sinθ)-2cos()

Multiply both sides by dθ

dh = -20  sinθ-2cos dθ

h  -20  sinθ-2cosθ

To determine

b)

To find:

The percentage error

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Problems 11-22, solve each system by elimination or by any convenient method.

Mathematical Applications for the Management, Life, and Social Sciences

#### π does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### 2 1 0 does not exist

Study Guide for Stewart's Multivariable Calculus, 8th 