Consider the circle with a 4 centimeter radius. If the length of major arc RT is
64/9π, what is the measure of ∠RST?
a.20
b.25
c.30
d.40

Respuesta :

Answer:

Option D is correct.i.e., ∠ RST = 40°

Step-by-step explanation:

Given: Radius of circle, r = 4 cm

           Center of circle is S and Length of Major ARC RT = [tex]\frac{64}{9}\times\pi[/tex]

To find: ∠ RST

Figure is attached

Let [tex]\theta[/tex] be the ∠ RST.

we use the formula of Length of Arc,

[tex]Length\: of\: Arc\: =\:\frac{\theta}{360^{\circ}}\times2\pi r[/tex]

We use this formula to find the angle made by arc RT at centre S,

[tex]Length\:of\:major\:Arc\:=\:\frac{360^{\circ}-\theta}{360^{\circ}}\times2\pi r[/tex]

[tex]\frac{64}{9}\times\pi=\:\frac{360^{\circ}-\theta}{360^{\circ}}\times2\pi \times4[/tex]

[tex]\frac{64}{9}\times\pi=\:\frac{360^{\circ}-\theta}{360^{\circ}}\times8\pi[/tex]

[tex]\frac{360^{\circ}-\theta}{360^{\circ}}=\frac{64\times\pi}{9\times8\pi}[/tex]

[tex]\frac{360^{\circ}-\theta}{360^{\circ}}=\frac{8}{9}[/tex]

[tex]360^{\circ}-\theta=\frac{8\times360}{9}[/tex]

[tex]360^{\circ}-\theta=8\times40[/tex]

[tex]360^{\circ}-\theta=320[/tex]

[tex]-\theta=320-360[/tex]

[tex]-\theta=-40[/tex]

[tex]\theta=40[/tex]

Therefore, Option D is correct.i.e., ∠ RST = 40°

Ver imagen aquialaska

Answer: 20

Step-by-step explanation:

Click link below for explanation.

Good Luck!

Ver imagen ddurcis