Answer:
a) Area of sector TRV = [tex] 42.4\: units^2 [/tex]
b) [tex] 0.8\: units[/tex]
Step-by-step explanation:
a)
In [tex] \odot R[/tex], TW is diameter.
Therefore,
[tex] m\widehat {TVW} = 180\degree [/tex]
[tex] \because m\widehat {TV} +m\widehat {VW} =m\widehat {TVW} [/tex]
[tex] \therefore m\widehat {TV} +120\degree =180\degree [/tex]
[tex] \therefore m\widehat {TV} =180\degree - 120\degree [/tex]
[tex] \therefore m\widehat {TV} = 60\degree [/tex]
[tex] \because m\angle TRV=m\widehat{TV} [/tex]
(Measure of central angle is equal to the measure of its corresponding arc)
[tex] \therefore m\angle TRV\:(\theta) =60\degree [/tex]
Radius (r) = RW = 9 units
Area of sector TRV
[tex] =\frac{\theta}{360\degree}\times \pi r^2 [/tex]
[tex] =\frac{60\degree}{360\degree} \times 3.14\times 9^2 [/tex]
[tex] =\frac{1}{6} \times 3.14\times 81 [/tex]
[tex] =\frac{1}{6} \times 254.34 [/tex]
[tex] =42.39\: units^2 [/tex]
Area of sector TRV[tex] =42.4\:units^2 [/tex]
b)
Length of [tex] \widehat{VW} [/tex]
[tex] =\frac{120\degree }{360\degree} \times 2\pi r [/tex]
[tex] =\frac{2}{3} \times 3.14\times 9 [/tex]
[tex] =2 \times 3.14\times 3 [/tex]
Length of [tex] \widehat{VW} [/tex] [tex] = 18.84\: units [/tex]
[tex] \overline{TW} =2*RW =2*9 = 18\: units[/tex]
[tex] \widehat{VW}- \overline{TW}= 18.84-18=0.84\: units[/tex]
[tex] \widehat{VW}- \overline{TW}= 0.8\: units[/tex]
