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Q. 72

Expert-verifiedFound in: Page 479

Book edition
7th Edition

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

Pages
948 pages

ISBN
9781337067508

**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 ${\mathit{\theta}}_{\mathbf{1}}$ at the point P, as shown in the first **

The value for ${\theta}_{1}$** is 1.047** and ${\theta}_{2}$ **is 1**.

The value for ${\theta}_{1}-{\theta}_{2}$ **is 0.47**.

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

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

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

Therefore ${\theta}_{1}=\frac{\pi}{3}$

Central angle incase of a sector is given by:

$s=r{\theta}_{2}$

${\theta}_{1}=\frac{\pi}{3}\phantom{\rule{0ex}{0ex}}{\theta}_{1}=1.047\phantom{\rule{0ex}{0ex}}{\theta}_{2}=\frac{s}{r}\phantom{\rule{0ex}{0ex}}{\theta}_{2}=\frac{1}{1}\phantom{\rule{0ex}{0ex}}{\theta}_{1}-{\theta}_{2}=1.047-1\phantom{\rule{0ex}{0ex}}=0.047$

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