## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 113: 64

#### Answer

If the land is circular, the radius is $~~549.8~m$ If the land is a $35^{\circ}$ sector, the radius of the circle is $~~1763.6~m$

#### Work Step by Step

Let's suppose that the land is a circle. We can find the radius $r$: $A = 950,000~m^2$ $\pi~r^2 = 950,000~m^2$ $r = \sqrt{\frac{950,000~m^2}{\pi}}$ $r = 549.8~m$ If the land is circular, the radius is $~~549.8~m$ Let's suppose the land is a $35^{\circ}$ sector. Then $\frac{35^{\circ}}{360^{\circ}}\times A = 950,000~m^2,~~$ where $A$ is the area of the whole circle. We can find the radius: $\frac{35^{\circ}}{360^{\circ}}\pi~r^2 = 950,000~m^2$ $r^2 = \frac{(360^{\circ})(950,000~m^2)}{(35^{\circ})(\pi)}$ $r = \sqrt{\frac{(360^{\circ})(950,000~m^2)}{(35^{\circ})(\pi)}}$ $r = 1763.6~m$ If the land is a $35^{\circ}$ sector, the radius of the circle is $~~1763.6~m$

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