Chapter 2.9, Problem 36E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

One side of a right triangle is known to be 20 cm long and the opposite angle is measured as

(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,

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

Use

Solve for h

**2) Given:**

3) **Calculation:**

Differentiate

By using power rule combined with the chain rule,

Multiply both sides by

Convert degrees in to radians

To determine

**b)**

**To find:**

The percentage error

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