Trig - Area?

[Amandaxox]

In the diagram below, find the area of the shaded sector. The circles are tangent to one another as shown in the diagram.

It's a multiple choice question. I got A, but I don't feel like it's correct.

A.) ?/2
B.) ?/3
C.) ?/4
D.) ?

 

[Deleted member 4993]

In the diagram below, find the area of the shaded sector. The circles are tangent to one another as shown in the diagram.

It's a multiple choice question. I got A, but I don't feel like it's correct.

A.) ?/2
B.) ?/3
C.) ?/4
D.) ?

ABC is a right angled triangle (3-4-5) - go from there.

 

[Amandaxox]

ABC is a right angled triangle (3-4-5) - go from there.

I'm aware it's right angled, I still don't understand how to solve it.

 

[Denis]

Well, since angle C = 90, I'll guess that makes shaded area = 1/4 of circle's area: agree ? :idea:

 

[Amandaxox]

Maybe I should rephrase my question...HOW DO I SOLVE THIS.

What I've tried so far is subtract 360 from 90 giving me 270 degrees then I converted it into radians and came up with 3/2 pi which obviously isn't correct

;|

 

[BigGlenntheHeavy]

\(\displaystyle The \ shaded \ area \ is \ a \ sector \ of \ a \ circle.\)

\(\displaystyle A_{sector} \ = \ \frac{\theta r^2}{2}, \ \theta \ in \ radians, \ r \ =1 \ and \ \theta \ = \ \frac{\pi}{2}.\)

 

[Deleted member 4993]

Go back to what Denis said:

since angle C = 90, I'll guess that makes shaded area = 1/4 of circle's area

If you knew the area of the circle (?r[sup:1zovvb3n]2[/sup:1zovvb3n]) - then you can find the area covered by the shade.

.