Chapter 9, Problem 21RP

a.

To determine

To calculate: The measure of angleDEF .

Answer to Problem 21RP

The measure of angleDEFis $90°$ .

Explanation of Solution

Given information:

Coordinates of vertex are $F\left(10,0\right).$

Formula used:

The measure ofarc for half a circle is $180°$ .

Calculation:

  

→DEF is half the measure of arc DF .

  $\begin{array}{l}m\angle DEF=\frac{1}{2}(m\stackrel{⌢}{DF})\\ =\frac{1}{2}({180}^{\circ })={90}^{\circ }\end{array}$

b.

To determine

To find: The measure of angleDEF .

Answer to Problem 21RP

The measure of angleDEF is ${180}^{\circ }$ .

Explanation of Solution

Given information:

Coordinates of vertex are $F\left(10,0\right).$

Formula used:

The measure of arc for half a circle is $180°$ .

Calculation:

  

The length of arc DEF is covered by half of a circle.

  $m\stackrel{⌢}{DEF}={180}^{\circ }$

c.

To determine

To calculate: The length of arc $\stackrel{⌢}{DEF}$ .

Answer to Problem 21RP

The length of arc $\stackrel{⌢}{DEF}$ is $10\pi$ .

Explanation of Solution

Given information:

Coordinates of vertex are $F\left(10,0\right).$

Formula used:

  $l(\stackrel{⌢}{RTC})=\frac{{180}^{\circ }}{{360}^{\circ }}(2\pi r)$

Calculation:

  

Coordinates of vertex are $F\left(10,0\right).$

  $\therefore r=10$

  $l(\stackrel{⌢}{DEF})=\frac{{180}^{\circ }}{{360}^{\circ }}(20\pi )=10\pi$