Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 113: 55


$3.6$ radians

Work Step by Step

Step 1: The formula to be used here will be $A=\frac{1}{2}r^{2}\theta$ where $A$ is the area of a sector of a circle of radius $r$ and central angle $\theta$. Step 2: Substituting the values provided by the question into the formula, $(16)=\frac{1}{2}(3)^{2}\theta$ Step 3: $16=\frac{9\theta}{2}$ Step 4: Multiplying both sides by $\frac{2}{9}$, $16\times\frac{2}{9}=\frac{9\theta}{2}\times\frac{2}{9}$ Step 5: $\theta=\frac{32}{9}=3.6$ radians
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