Find the area of the sector of a circle of radius 16 units subtended by an angle of 300°. Round your answer to the nearesttenth, and do not include the units in your answer.

Answered: Find the area of the sector of a circle…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

Find the area of the sector of a circle of radius 16 units subtended by an angle of 300°. Round your answer to the nearest
tenth, and do not include the units in your answer.

Expert Solution

Step 1

Given

radius of circle (r)= 16 unit

angle made by arc to center of circle $\emptyset$ =300⁰

$= 300 * \frac{π}{180} = \frac{5 π}{3} r a d i a n$

$W e k n o w t h a t a r e a o f s e c t o r = \frac{1}{2} r^{2} \emptyset = \frac{1}{2} * 16^{2} * \frac{5 π}{3} = \frac{1}{2} * 16 * 16 * \frac{5 π}{3} = 640 * \frac{π}{3} = 640 * \frac{22}{7 * 3} = 670.476 sq . unit$

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Find the area of the sector of a circle of radius 16 units subtended by an angle of 300°. Round your answer to the nearest tenth, and do not include the units in your answer.