   Chapter 14, Problem 34RE

Chapter
Section
Textbook Problem

The two legs of a right triangle are measured as 5 m and 12 m with a possible error in measurement of at most 0.2 cm in each. Use differentials to estimate the maximum error in the calculated value of (a) the area of the triangle and (b) the length of the hypotenuse.

(a)

To determine

To estimate: The maximum error in the calculated areaof triangle by using differential.

Explanation

Given:

The area of triangle is A=12ab .

Where aandb are two legs of the triangle.

The value of a is 5m .

The value of b is 12m .

The errors in aandb are 0.2cm .

Calculation:

The given function is A=12ab (1)

The differential function dA is defined by, dA=Aada+Abdb .

Take partial derivative with respect to a in the equation (1),

Aa=a(12ab)=(12)(1)(b)=b2

Thus, Aa=b2

(b)

To determine

To estimate: The maximum error in the calculated length of hypotenuse of the triangle by using differential.

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