Chapter 9.2, Problem 3PSA

a

To determine

To find:The measure of the arc EF

Answer to Problem 3PSA

The measure of the arc EF is $m\stackrel{⌢}{EF}={180}^0$

Explanation of Solution

Given information:The following information has been given

Center of the circle is a origin

Radius of the circle is four units

Calculation:We know that the measure of an arc is the degree measure subtended by the arc to the center of the circle. Hence, the angle subtended by the arc is same as the angle between the X and − X axes. Hence, we can say that

  $m\stackrel{⌢}{EF}={180}^0$

b

To determine

To find:The length of the arc EF to the nearest tenth

Answer to Problem 3PSA

The length of the arc $\stackrel{⌢}{EF}=12.6$

Explanation of Solution

Given information:The following information has been given

Center of the circle is a origin

Radius of the circle is five units $(r=5)$

Formula used:The length of any arc can be found by

  $\stackrel{⌢}{CD}=2\pi r\frac{\theta }{{360}^0}$

Where $\theta$ is the angle subtended by the arc on the center of the circle.

Calculation:We know that the length of the arc can be found by

  $\stackrel{⌢}{EF}=2\pi r\frac{{180}^0}{{360}^0}$

Hence, we substitute the value of radius from the given information, and we get

  $\stackrel{⌢}{EF}=\frac{8\pi }{2}=12.566$