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Q. 72

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Precalculus Mathematics for Calculus

Found in: Page 479

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

Comparing a Triangle and a Sector of a Circle Two wood sticks and a metal rod, each of length 1, are connected to form a triangle with angle $θ_{1}$ at the point P, as shown in the first figure below. The rod is then bent to form an arc of a circle with center P, resulting in a smaller angle $θ_{2}$ at the point P, as shown in the second figure. Find $θ_{1}$ , $θ_{2}$ , and $θ_{1} - θ_{2}$ .

The value for $θ_{1}$ is 1.047 and $θ_{2}$ is 1.

The value for $θ_{1} - θ_{2}$ is 0.47.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Since, first figure is an equilateral triangle therefore each angle is $60^{\circ}$ i.e. $\frac{π}{3}$

Radius and sides is 1unit in case of both the figures.

Step 2. Write the concept.

Equilateral triangle has angle equal to $60^{\circ}$

Therefore $θ_{1} = \frac{π}{3}$

Central angle incase of a sector is given by:

$s = r θ_{2}$

Step 3. Determining the values.

$θ_{1} = \frac{π}{3} θ_{1} = 1.047 θ_{2} = \frac{s}{r} θ_{2} = \frac{1}{1} θ_{1} - θ_{2} = 1.047 - 1 = 0 .047$

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