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Geometry question w/ a Circle. find area of a shaded region. (Harder problem)
 one year ago
 one year ago
Geometry question w/ a Circle. find area of a shaded region. (Harder problem)
 one year ago
 one year ago

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LethalBest ResponseYou've already chosen the best response.0
I think what you have to do is to bisect the triangle into 60 degree up top and then the bottom left and right are still 30 degrees. then you do the 30 60 90 triangle thing.
 one year ago

alexwee123Best ResponseYou've already chosen the best response.1
i did it a different way...
 one year ago

LethalBest ResponseYou've already chosen the best response.0
well. it shouldn't be that complicated im only doing geometry.
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
Area of minor segment \[A = \frac{1}{2} r^2 \left(\theta\sin\theta\right) \] But the only problem is \(r\) is not given..
 one year ago

HeroBest ResponseYou've already chosen the best response.0
I think I meant to post the area of a sector of a circle
 one year ago

LethalBest ResponseYou've already chosen the best response.0
you guys are thinking too hard its only like subtracting a sector
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
Area of sector  area of triangle
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
But \(r\) is not given!!! Im thinking of using the cosine rule and sine rule to find \(r\) would it work?
 one year ago

LethalBest ResponseYou've already chosen the best response.0
here ill take it a bit further. dw:1345780578744:dw does that help?
 one year ago

HeroBest ResponseYou've already chosen the best response.0
It will not be hard to find \(r\)
 one year ago

HeroBest ResponseYou've already chosen the best response.0
Is the vertex of angle 120 is the center of the circle?
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
dw:1345780720301:dw looks like you can use the sine rule..
 one year ago

HeroBest ResponseYou've already chosen the best response.0
Okay, so yeah just do Area of Sector  Area of Triangle like what @Mimi_x3 suggested
 one year ago

LethalBest ResponseYou've already chosen the best response.0
soo all we need is the area of the circle and then we can use the 120/360 * pi r2 or something and subtract the area from that.
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
I got 8 as well using the sine rule
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
Now its easy..you can do it yourself
 one year ago

LethalBest ResponseYou've already chosen the best response.0
ok so 64 pi is the area of the circle
 one year ago

LethalBest ResponseYou've already chosen the best response.0
and the area of the triangle left side is 1/2 * 4sqroot3 * 4
 one year ago

LethalBest ResponseYou've already chosen the best response.0
*2 to make up for the other side.
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
I will just use this formula\[A = \frac{1}{2} r^2 \left(\theta\sin\theta\right) \] No need to derive it
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
and it must be in radians..so convert it..
 one year ago

alexwee123Best ResponseYou've already chosen the best response.1
you guys are thinking too hard o.0
 one year ago

LethalBest ResponseYou've already chosen the best response.0
oh wait i got the answer. just do 120/360 which is 1/3 and then i did 1/3 * 64pi which is the area of the circle and it is 64pi/3 and now subtract it by the area of the triangle which is
 one year ago

LethalBest ResponseYou've already chosen the best response.0
1/2 4sqrt3 * 4 or 8sqrt3 * 2 for the other side
 one year ago

alexwee123Best ResponseYou've already chosen the best response.1
dw:1345781211630:dw dw:1345781273195:dw
 one year ago

alexwee123Best ResponseYou've already chosen the best response.1
dw:1345781325118:dw
 one year ago

LethalBest ResponseYou've already chosen the best response.0
so the final answer is \[64\pi/3  16\sqrt{3}\]
 one year ago

alexwee123Best ResponseYou've already chosen the best response.1
yes good job @Lethal
 one year ago

LethalBest ResponseYou've already chosen the best response.0
yep, i would best response both of u but i can only do one. thx alex.
 one year ago
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