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Q. 72

Precalculus Mathematics for Calculus
Found in: Page 479
Precalculus Mathematics for Calculus

Precalculus Mathematics for Calculus

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 θ1 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 θ2 at the point P, as shown in the second figure. Find θ1, θ2, and θ1θ2.

The value for θ1 is 1.047 and θ2 is 1.

The value for θ1θ2 is 0.47.

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Step by Step Solution

Step 1. Given information.

Since, first figure is an equilateral triangle therefore each angle is 60 i.e. π3

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

Step 2. Write the concept.

Equilateral triangle has angle equal to 60

Therefore θ1=π3

Central angle incase of a sector is given by:


Step 3. Determining the values.

θ1=π3θ1=1.047θ2=srθ2=11θ1θ2=1.0471 =0.047

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