Math question! Help!

[rafae]

Hey, can someone solve this question?

Before you begin, i'll tell you abit of information.
All three vertices of the triangle are touching the circumference of the circle, and therefore the triangle is not as correctly drawn.

What the question asks is to find the percentage of the shaded area as a percentage of the whole circle.

That is the the only information given. Please help!

 

[abcde]

My answer comes as 58.7%. Is this correct? If so, I'll explain.

 

[rafae]

Yes, it is correct.

 

[abcde]

Seriously?
First I found out the area of the triangle: 3 x 1/2 x r^2 x sin(360/3) = 1.299038106 r^2.
=> Shaded Area = (pi r^2) - (1.299038106 r^2) = r^2 (pi - 1.299038106) = 1.842554548 r^2.
=> Percentage of shaded are as a percentage of the whole circle = (1.842554548 r^2/ pi r^2) x 100%
The r^2 gets cancelled and when you evaluate using your calculator, the answer is approximately 58.7 % (correct to 3 sig. fig.)
Hope this helped.

 

[CaptainDanger]

Seriously?
First I found out the area of the triangle: 3 x 1/2 x r^2 x sin(360/3) = 1.299038106 r^2.
=> Shaded Area = (pi r^2) - (1.299038106 r^2) = r^2 (pi - 1.299038106) = 1.842554548 r^2.
=> Percentage of shaded are as a percentage of the whole circle = (1.842554548 r^2/ pi r^2) x 100%
The r^2 gets cancelled and when you evaluate using your calculator, the answer is approximately 58.7 % (correct to 3 sig. fig.)
Hope this helped.

Hey ,

What is that formula you used to find out the triangle area???

I know about finding it using Sine Formula... But I don't get this??? 360/3??? And 3 in the start of it? For equilateral triangle it should be 180/3...

 

[abcde]

I saw the triangle inscribed in the circle as being made up of 3 inner triangles each of which have the radius (of the circle) as two of its sides and an angle of 120* between them.
Is it clear now?

 

[CaptainDanger]

Yes.. Thnks...